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Publisher: Springer-Verlag   (Total: 2335 journals)

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Showing 1 - 200 of 2335 Journals sorted alphabetically
3D Research     Hybrid Journal   (Followers: 19, SJR: 0.214, h-index: 10)
4OR: A Quarterly J. of Operations Research     Hybrid Journal   (Followers: 9, SJR: 1.073, h-index: 25)
AAPS J.     Hybrid Journal   (Followers: 16, SJR: 1.192, h-index: 74)
AAPS PharmSciTech     Hybrid Journal   (Followers: 6, SJR: 0.718, h-index: 54)
Abdominal Imaging     Hybrid Journal   (Followers: 16, SJR: 0.723, h-index: 60)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2, SJR: 0.447, h-index: 12)
Academic Psychiatry     Full-text available via subscription   (Followers: 22, SJR: 0.492, h-index: 32)
Academic Questions     Hybrid Journal   (Followers: 7, SJR: 0.135, h-index: 6)
Accreditation and Quality Assurance: J. for Quality, Comparability and Reliability in Chemical Measurement     Hybrid Journal   (Followers: 26, SJR: 0.378, h-index: 30)
Acoustical Physics     Hybrid Journal   (Followers: 10, SJR: 0.355, h-index: 20)
Acta Analytica     Hybrid Journal   (Followers: 7, SJR: 0.387, h-index: 6)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1, SJR: 0.624, h-index: 34)
Acta Biotheoretica     Hybrid Journal   (Followers: 5, SJR: 0.419, h-index: 25)
Acta Diabetologica     Hybrid Journal   (Followers: 14, SJR: 1.318, h-index: 46)
Acta Endoscopica     Hybrid Journal   (Followers: 1, SJR: 0.113, h-index: 8)
acta ethologica     Hybrid Journal   (Followers: 4, SJR: 0.465, h-index: 23)
Acta Geochimica     Hybrid Journal   (Followers: 3)
Acta Geodaetica et Geophysica     Hybrid Journal   (Followers: 1, SJR: 0.294, h-index: 13)
Acta Geotechnica     Hybrid Journal   (Followers: 6, SJR: 1.818, h-index: 22)
Acta Informatica     Hybrid Journal   (Followers: 5, SJR: 0.524, h-index: 32)
Acta Mathematica     Hybrid Journal   (Followers: 10, SJR: 8.021, h-index: 47)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2, SJR: 0.53, h-index: 29)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5, SJR: 0.406, h-index: 30)
Acta Mathematica Vietnamica     Hybrid Journal   (SJR: 0.451, h-index: 5)
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal   (SJR: 0.22, h-index: 20)
Acta Mechanica     Hybrid Journal   (Followers: 18, SJR: 0.898, h-index: 52)
Acta Mechanica Sinica     Hybrid Journal   (Followers: 4, SJR: 0.426, h-index: 29)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 5, SJR: 0.525, h-index: 18)
Acta Meteorologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.524, h-index: 14)
Acta Neurochirurgica     Hybrid Journal   (Followers: 7, SJR: 0.833, h-index: 73)
Acta Neurologica Belgica     Hybrid Journal   (SJR: 0.348, h-index: 27)
Acta Neuropathologica     Hybrid Journal   (Followers: 3, SJR: 6.61, h-index: 117)
Acta Oceanologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.295, h-index: 17)
Acta Parasitologica     Hybrid Journal   (Followers: 9, SJR: 0.581, h-index: 28)
Acta Physiologiae Plantarum     Hybrid Journal   (Followers: 2, SJR: 0.551, h-index: 39)
Acta Politica     Hybrid Journal   (Followers: 13, SJR: 0.658, h-index: 20)
adhäsion KLEBEN & DICHTEN     Hybrid Journal   (Followers: 5, SJR: 0.103, h-index: 4)
ADHD Attention Deficit and Hyperactivity Disorders     Hybrid Journal   (Followers: 20, SJR: 0.871, h-index: 15)
Adhesion Adhesives & Sealants     Hybrid Journal   (Followers: 7)
Administration and Policy in Mental Health and Mental Health Services Research     Partially Free   (Followers: 15, SJR: 0.795, h-index: 40)
Adsorption     Hybrid Journal   (Followers: 4, SJR: 0.774, h-index: 52)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3, SJR: 0.319, h-index: 15)
Advances in Atmospheric Sciences     Hybrid Journal   (Followers: 34, SJR: 0.959, h-index: 44)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15, SJR: 1.255, h-index: 44)
Advances in Contraception     Hybrid Journal   (Followers: 2)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 48, SJR: 1.113, h-index: 14)
Advances in Gerontology     Partially Free   (Followers: 7, SJR: 0.141, h-index: 3)
Advances in Health Sciences Education     Hybrid Journal   (Followers: 23, SJR: 1.397, h-index: 42)
Advances in Manufacturing     Hybrid Journal   (Followers: 3, SJR: 0.2, h-index: 4)
Advances in Polymer Science     Hybrid Journal   (Followers: 40, SJR: 0.637, h-index: 89)
Advances in Therapy     Hybrid Journal   (Followers: 6, SJR: 0.79, h-index: 44)
Aegean Review of the Law of the Sea and Maritime Law     Hybrid Journal   (Followers: 7)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2, SJR: 0.882, h-index: 23)
Aerobiologia     Hybrid Journal   (Followers: 1, SJR: 0.511, h-index: 36)
Aesthetic Plastic Surgery     Hybrid Journal   (Followers: 8, SJR: 0.821, h-index: 49)
African Archaeological Review     Hybrid Journal   (Followers: 14, SJR: 0.612, h-index: 24)
Afrika Matematika     Hybrid Journal   (Followers: 1, SJR: 0.248, h-index: 6)
AGE     Hybrid Journal   (Followers: 7, SJR: 1.358, h-index: 33)
Ageing Intl.     Hybrid Journal   (Followers: 6, SJR: 0.337, h-index: 10)
Aggiornamenti CIO     Hybrid Journal   (Followers: 1)
Aging Clinical and Experimental Research     Hybrid Journal   (Followers: 3, SJR: 0.529, h-index: 55)
Agricultural Research     Hybrid Journal   (Followers: 3)
Agriculture and Human Values     Hybrid Journal   (Followers: 12, SJR: 1.197, h-index: 49)
Agroforestry Systems     Hybrid Journal   (Followers: 20, SJR: 0.64, h-index: 56)
Agronomy for Sustainable Development     Hybrid Journal   (Followers: 10, SJR: 1.732, h-index: 59)
AI & Society     Hybrid Journal   (Followers: 7, SJR: 0.171, h-index: 19)
AIDS and Behavior     Hybrid Journal   (Followers: 13, SJR: 2.006, h-index: 71)
Air Quality, Atmosphere & Health     Hybrid Journal   (Followers: 2, SJR: 0.706, h-index: 19)
Akupunktur & Aurikulomedizin     Full-text available via subscription   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2, SJR: 0.566, h-index: 18)
Algebra Universalis     Hybrid Journal   (Followers: 2, SJR: 0.388, h-index: 22)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1, SJR: 0.868, h-index: 20)
Algorithmica     Hybrid Journal   (Followers: 7, SJR: 0.898, h-index: 56)
Allergo J.     Full-text available via subscription   (Followers: 1, SJR: 0.183, h-index: 20)
Allergo J. Intl.     Hybrid Journal   (Followers: 2)
Alpine Botany     Hybrid Journal   (Followers: 3, SJR: 0.729, h-index: 20)
ALTEX : Alternatives to Animal Experimentation     Open Access   (Followers: 3, SJR: 1.392, h-index: 32)
AMBIO     Hybrid Journal   (Followers: 14, SJR: 1.094, h-index: 87)
American J. of Cardiovascular Drugs     Hybrid Journal   (Followers: 10, SJR: 0.864, h-index: 39)
American J. of Community Psychology     Hybrid Journal   (Followers: 24, SJR: 1.237, h-index: 83)
American J. of Criminal Justice     Hybrid Journal   (Followers: 5, SJR: 0.634, h-index: 13)
American J. of Cultural Sociology     Hybrid Journal   (Followers: 11, SJR: 0.283, h-index: 3)
American J. of Dance Therapy     Hybrid Journal   (Followers: 4, SJR: 0.175, h-index: 13)
American J. of Potato Research     Hybrid Journal   (Followers: 2, SJR: 0.558, h-index: 35)
American J. of Psychoanalysis     Hybrid Journal   (Followers: 20, SJR: 0.293, h-index: 13)
American Sociologist     Hybrid Journal   (Followers: 10, SJR: 0.18, h-index: 13)
Amino Acids     Hybrid Journal   (Followers: 8, SJR: 1.362, h-index: 83)
AMS Review     Partially Free   (Followers: 4)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 5, SJR: 0.21, h-index: 37)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4, SJR: 0.665, h-index: 7)
Analysis in Theory and Applications     Hybrid Journal  
Analysis of Verbal Behavior     Hybrid Journal   (Followers: 4)
Analytical and Bioanalytical Chemistry     Hybrid Journal   (Followers: 32, SJR: 1.096, h-index: 123)
Anatomical Science Intl.     Hybrid Journal   (Followers: 2, SJR: 0.301, h-index: 26)
Angewandte Schmerztherapie und Palliativmedizin     Hybrid Journal  
Angiogenesis     Hybrid Journal   (Followers: 3, SJR: 2.212, h-index: 69)
Animal Cognition     Hybrid Journal   (Followers: 13, SJR: 1.122, h-index: 55)
Annales françaises de médecine d'urgence     Hybrid Journal   (Followers: 1, SJR: 0.156, h-index: 4)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3, SJR: 1.377, h-index: 32)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annali dell'Universita di Ferrara     Hybrid Journal   (SJR: 0.504, h-index: 14)
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1, SJR: 1.167, h-index: 26)
Annals of Behavioral Medicine     Hybrid Journal   (Followers: 10, SJR: 2.112, h-index: 98)
Annals of Biomedical Engineering     Hybrid Journal   (Followers: 18, SJR: 1.182, h-index: 94)
Annals of Combinatorics     Hybrid Journal   (Followers: 3, SJR: 0.849, h-index: 15)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Dyslexia     Hybrid Journal   (Followers: 9, SJR: 0.857, h-index: 40)
Annals of Finance     Hybrid Journal   (Followers: 27, SJR: 0.686, h-index: 14)
Annals of Forest Science     Hybrid Journal   (Followers: 4, SJR: 0.929, h-index: 57)
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1, SJR: 1.136, h-index: 23)
Annals of Hematology     Hybrid Journal   (Followers: 13, SJR: 1.117, h-index: 62)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6, SJR: 0.593, h-index: 42)
Annals of Microbiology     Hybrid Journal   (Followers: 9, SJR: 0.402, h-index: 26)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 5, SJR: 0.68, h-index: 45)
Annals of Operations Research     Hybrid Journal   (Followers: 8, SJR: 1.186, h-index: 78)
Annals of Regional Science     Hybrid Journal   (Followers: 7, SJR: 0.405, h-index: 42)
Annals of Software Engineering     Hybrid Journal   (Followers: 12)
Annals of Solid and Structural Mechanics     Hybrid Journal   (Followers: 9, SJR: 0.553, h-index: 8)
Annals of Surgical Oncology     Hybrid Journal   (Followers: 11, SJR: 1.902, h-index: 127)
Annals of Telecommunications     Hybrid Journal   (Followers: 7, SJR: 0.315, h-index: 25)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.931, h-index: 31)
Antonie van Leeuwenhoek     Hybrid Journal   (Followers: 5, SJR: 0.992, h-index: 87)
Apidologie     Hybrid Journal   (Followers: 4, SJR: 1.14, h-index: 57)
APOPTOSIS     Hybrid Journal   (Followers: 7, SJR: 1.554, h-index: 87)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2, SJR: 0.354, h-index: 27)
Applications of Mathematics     Hybrid Journal   (Followers: 1, SJR: 0.274, h-index: 20)
Applied Biochemistry and Biotechnology     Hybrid Journal   (Followers: 44, SJR: 0.575, h-index: 80)
Applied Biochemistry and Microbiology     Hybrid Journal   (Followers: 17, SJR: 0.267, h-index: 26)
Applied Categorical Structures     Hybrid Journal   (Followers: 2, SJR: 0.361, h-index: 21)
Applied Composite Materials     Hybrid Journal   (Followers: 45, SJR: 0.705, h-index: 35)
Applied Entomology and Zoology     Partially Free   (Followers: 2, SJR: 0.554, h-index: 34)
Applied Geomatics     Hybrid Journal   (Followers: 3, SJR: 0.323, h-index: 9)
Applied Geophysics     Hybrid Journal   (Followers: 7, SJR: 0.541, h-index: 13)
Applied Intelligence     Hybrid Journal   (Followers: 13, SJR: 0.777, h-index: 43)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 3, SJR: 0.358, h-index: 34)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4, SJR: 0.955, h-index: 33)
Applied Mathematics - A J. of Chinese Universities     Hybrid Journal   (SJR: 0.275, h-index: 8)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 4, SJR: 0.37, h-index: 26)
Applied Microbiology and Biotechnology     Hybrid Journal   (Followers: 61, SJR: 1.262, h-index: 161)
Applied Physics A     Hybrid Journal   (Followers: 8, SJR: 0.535, h-index: 121)
Applied Physics B: Lasers and Optics     Hybrid Journal   (Followers: 22, SJR: 0.983, h-index: 104)
Applied Psychophysiology and Biofeedback     Hybrid Journal   (Followers: 6, SJR: 0.677, h-index: 47)
Applied Research in Quality of Life     Hybrid Journal   (Followers: 10, SJR: 0.288, h-index: 15)
Applied Solar Energy     Hybrid Journal   (Followers: 16, SJR: 0.251, h-index: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4, SJR: 0.351, h-index: 9)
Aquaculture Intl.     Hybrid Journal   (Followers: 21, SJR: 0.613, h-index: 40)
Aquarium Sciences and Conservation     Hybrid Journal   (Followers: 1)
Aquatic Ecology     Hybrid Journal   (Followers: 31, SJR: 0.646, h-index: 44)
Aquatic Geochemistry     Hybrid Journal   (Followers: 3, SJR: 0.764, h-index: 39)
Aquatic Sciences     Hybrid Journal   (Followers: 12, SJR: 1.172, h-index: 53)
Arabian J. for Science and Engineering     Hybrid Journal   (Followers: 5, SJR: 0.345, h-index: 20)
Arabian J. of Geosciences     Hybrid Journal   (Followers: 1, SJR: 0.417, h-index: 16)
Archaeological and Anthropological Sciences     Hybrid Journal   (Followers: 21, SJR: 1.056, h-index: 15)
Archaeologies     Hybrid Journal   (Followers: 12, SJR: 0.397, h-index: 13)
Archiv der Mathematik     Hybrid Journal   (Followers: 1, SJR: 0.597, h-index: 29)
Archival Science     Hybrid Journal   (Followers: 51, SJR: 0.804, h-index: 22)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 7, SJR: 0.28, h-index: 15)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1, SJR: 0.946, h-index: 23)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (SJR: 4.091, h-index: 66)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4, SJR: 0.865, h-index: 40)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4, SJR: 2.841, h-index: 40)
Archives of Dermatological Research     Hybrid Journal   (Followers: 6, SJR: 0.9, h-index: 65)
Archives of Environmental Contamination and Toxicology     Hybrid Journal   (Followers: 10, SJR: 0.846, h-index: 84)
Archives of Gynecology and Obstetrics     Hybrid Journal   (Followers: 16, SJR: 0.695, h-index: 47)
Archives of Microbiology     Hybrid Journal   (Followers: 8, SJR: 0.702, h-index: 85)
Archives of Orthopaedic and Trauma Surgery     Hybrid Journal   (Followers: 8, SJR: 1.039, h-index: 56)
Archives of Osteoporosis     Hybrid Journal   (Followers: 2, SJR: 1.092, h-index: 13)
Archives of Sexual Behavior     Hybrid Journal   (Followers: 9, SJR: 1.198, h-index: 74)
Archives of Toxicology     Hybrid Journal   (Followers: 16, SJR: 1.595, h-index: 76)
Archives of Virology     Hybrid Journal   (Followers: 4, SJR: 1.086, h-index: 90)
Archives of Women's Mental Health     Hybrid Journal   (Followers: 13, SJR: 1.264, h-index: 50)
Archivio di Ortopedia e Reumatologia     Hybrid Journal  
Archivum Immunologiae et Therapiae Experimentalis     Hybrid Journal   (Followers: 2, SJR: 1.2, h-index: 42)
ArgoSpine News & J.     Hybrid Journal   (SJR: 0.102, h-index: 3)
Argumentation     Hybrid Journal   (Followers: 4, SJR: 0.295, h-index: 18)
Arid Ecosystems     Hybrid Journal   (Followers: 3)
Arkiv för Matematik     Hybrid Journal   (Followers: 1, SJR: 0.948, h-index: 22)
Arnold Mathematical J.     Hybrid Journal   (Followers: 1)
Arthropod-Plant Interactions     Hybrid Journal   (Followers: 2, SJR: 0.797, h-index: 17)
Arthroskopie     Hybrid Journal   (Followers: 1, SJR: 0.145, h-index: 8)
Artificial Intelligence and Law     Hybrid Journal   (Followers: 8, SJR: 0.288, h-index: 25)
Artificial Intelligence Review     Hybrid Journal   (Followers: 15, SJR: 0.948, h-index: 48)
Artificial Life and Robotics     Hybrid Journal   (Followers: 8, SJR: 0.231, h-index: 14)
Asia Europe J.     Hybrid Journal   (Followers: 4, SJR: 0.247, h-index: 9)
Asia Pacific Education Review     Hybrid Journal   (Followers: 9, SJR: 0.371, h-index: 17)
Asia Pacific J. of Management     Hybrid Journal   (Followers: 11, SJR: 1.676, h-index: 50)
Asia-Pacific Education Researcher     Hybrid Journal   (Followers: 11, SJR: 0.353, h-index: 13)
Asia-Pacific Financial Markets     Hybrid Journal   (Followers: 2, SJR: 0.19, h-index: 15)
Asia-Pacific J. of Atmospheric Sciences     Hybrid Journal   (Followers: 20, SJR: 1.006, h-index: 14)
Asian Business & Management     Hybrid Journal   (Followers: 7, SJR: 0.41, h-index: 10)
Asian J. of Business Ethics     Hybrid Journal   (Followers: 7)
Asian J. of Criminology     Hybrid Journal   (Followers: 5, SJR: 0.263, h-index: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 2, SJR: 0.681, h-index: 15)
AStA Wirtschafts- und Sozialstatistisches Archiv     Hybrid Journal   (Followers: 5, SJR: 0.195, h-index: 5)
ästhetische dermatologie & kosmetologie     Full-text available via subscription  
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 21, SJR: 4.511, h-index: 44)
Astronomy Letters     Hybrid Journal   (Followers: 19, SJR: 0.58, h-index: 30)
Astronomy Reports     Hybrid Journal   (Followers: 12, SJR: 0.473, h-index: 23)
Astrophysical Bulletin     Hybrid Journal   (Followers: 2, SJR: 0.469, h-index: 11)
Astrophysics     Hybrid Journal   (Followers: 22, SJR: 0.243, h-index: 11)

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Journal Cover Archive for Rational Mechanics and Analysis
  [SJR: 4.091]   [H-I: 66]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0673 - ISSN (Online) 0003-9527
   Published by Springer-Verlag Homepage  [2335 journals]
  • Locality of the Thomas–Fermi–von Weizsäcker Equations
    • Authors: F. Q. Nazar; C. Ortner
      Pages: 817 - 870
      Abstract: Abstract We establish a pointwise stability estimate for the Thomas–Fermi–von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas–Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1075-6
      Issue No: Vol. 224, No. 3 (2017)
  • On the Critical One Component Regularity for 3-D Navier-Stokes System:
           General Case
    • Authors: Jean-Yves Chemin; Ping Zhang; Zhifei Zhang
      Pages: 871 - 905
      Abstract: Abstract Let us consider initial data \({v_0}\) for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to \({L^{\frac 32}\cap L^2}\) . We prove that if the solution associated with \({v_0}\) blows up at a finite time \({T^\star}\) , then for any p in \({]4,\infty[}\) , and any unit vector e of \({\mathbb{R}^3}\) , the L p norm in time with value in \({\dot{H}^{\frac 12+\frac 2 p }}\) of \({(v e)_{\mathbb{R}^3}}\) blows up at \({T^\star}\) .
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1089-0
      Issue No: Vol. 224, No. 3 (2017)
  • Connecting Atomistic and Continuous Models of Elastodynamics
    • Authors: Julian Braun
      Pages: 907 - 953
      Abstract: Abstract We prove the long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the interatomic distances tend to zero. Here, the continuum energy density is given by the Cauchy–Born rule. The models considered allow for general finite range interactions. To control the stability of large deformations we also prove a new atomistic Gårding inequality.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1091-6
      Issue No: Vol. 224, No. 3 (2017)
  • A Partial Differential Equation for the Rank One Convex Envelope
    • Authors: Adam M. Oberman; Yuanlong Ruan
      Pages: 955 - 984
      Abstract: Abstract A partial differential equation (PDE) for the rank one convex envelope is introduced. The existence and uniqueness of viscosity solutions to the PDE is established. Elliptic finite difference schemes are constructed and convergence of finite difference solutions to the viscosity solution of the PDE is proven. Computational results are presented and laminates are computed from the envelopes. Results include the Kohn–Strang example, the classical four gradient example, and an example with eight gradients which produces nontrivial laminates.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1092-5
      Issue No: Vol. 224, No. 3 (2017)
  • Energy Scaling Law for a Single Disclination in a Thin Elastic Sheet
    • Authors: Heiner Olbermann
      Pages: 985 - 1019
      Abstract: Abstract We consider a single disclination in a thin elastic sheet of thickness h. We prove ansatz-free lower bounds for the free elastic energy in three different settings: first, for a geometrically fully non-linear plate model; second, for three-dimensional nonlinear elasticity; and third, for the Föppl-von Kármán plate theory. The lower bounds in the first and third result are optimal in the sense that we find upper bounds that are identical to the respective lower bounds in the leading order of h.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1093-4
      Issue No: Vol. 224, No. 3 (2017)
  • Cusp Formation for a Nonlocal Evolution Equation
    • Authors: Vu Hoang; Maria Radosz
      Pages: 1021 - 1036
      Abstract: Abstract Córdoba et al. (Ann Math 162(3):1377–1389, 2005) introduced a nonlocal active scalar equation as a one-dimensional analogue of the surface-quasigeostrophic equation. It has been conjectured, based on numerical evidence, that the solution forms a cusp-like singularity in finite time. Up until now, no active scalar with nonlocal flux is known for which cusp formation has been rigorously shown. In this paper, we introduce and study a nonlocal active scalar, inspired by the Córdoba–Córdoba–Fontelos equation, and prove that either a cusp- or needle-like singularity forms in finite time.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1094-3
      Issue No: Vol. 224, No. 3 (2017)
  • Optimal Boundary Control of a Simplified Ericksen–Leslie System for
           Nematic Liquid Crystal Flows in 2 D
    • Authors: Cecilia Cavaterra; Elisabetta Rocca; Hao Wu
      Pages: 1037 - 1086
      Abstract: Abstract In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen–Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity coupled with a convective Ginzburg–Landau type equation for the averaged molecular orientation. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the molecular orientation is subject to a time-dependent Dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals. We first establish the existence of optimal boundary controls. Then we show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1095-2
      Issue No: Vol. 224, No. 3 (2017)
  • Characterization of Generalized Young Measures Generated by Symmetric
    • Authors: Guido De Philippis; Filip Rindler
      Pages: 1087 - 1125
      Abstract: Abstract This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer–Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The “local” proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti’s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1096-1
      Issue No: Vol. 224, No. 3 (2017)
  • Mass–Radius Spirals for Steady State Families of the
           Vlasov–Poisson System
    • Authors: Tobias Ramming; Gerhard Rein
      Pages: 1127 - 1159
      Abstract: Abstract We consider spherically symmetric steady states of the Vlasov–Poisson system, which describe equilibrium configurations of galaxies or globular clusters. If the microscopic equation of state, i.e., the dependence of the steady state on the particle energy (and angular momentum) is fixed, a one-parameter family of such states is obtained. In the polytropic case the mass of the state along such a one-parameter family is a monotone function of its radius. We prove that for the King, Woolley–Dickens, and related models this mass–radius relation takes the form of a spiral.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1098-z
      Issue No: Vol. 224, No. 3 (2017)
  • Enhanced Dissipation, Hypoellipticity, and Anomalous Small Noise Inviscid
           Limits in Shear Flows
    • Authors: Jacob Bedrossian; Michele Coti Zelati
      Pages: 1161 - 1204
      Abstract: Abstract We analyze the decay and instant regularization properties of the evolution semigroups generated by two-dimensional drift-diffusion equations in which the scalar is advected by a shear flow and dissipated by full or partial diffusion. We consider both the space-periodic \({\mathbb{T}^2}\) setting and the case of a bounded channel \({\mathbb{T} \times [0,1]}\) with no-flux boundary conditions. In the infinite Péclet number limit (diffusivity \({\nu\to 0}\) ), our work quantifies the enhanced dissipation effect due to the shear. We also obtain hypoelliptic regularization, showing that solutions are instantly Gevrey regular even with only partial diffusion. The proofs rely on localized spectral gap inequalities and ideas from hypocoercivity with an augmented energy functional with weights replaced by pseudo-differential operators (of a rather simple form). As an application, we study small noise inviscid limits of invariant measures of stochastic perturbations of passive scalars, and show that the classical Freidlin scaling between noise and diffusion can be modified. In particular, although statistically stationary solutions blow up in \({H^1}\) in the limit \({\nu \to 0}\) , we show that viscous invariant measures still converge to a unique inviscid measure.
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1099-y
      Issue No: Vol. 224, No. 3 (2017)
  • Boundary Korn Inequality and Neumann Problems in Homogenization of Systems
           of Elasticity
    • Authors: Jun Geng; Zhongwei Shen; Liang Song
      Pages: 1205 - 1236
      Abstract: Abstract This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L 2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).
      PubDate: 2017-06-01
      DOI: 10.1007/s00205-017-1103-6
      Issue No: Vol. 224, No. 3 (2017)
  • Nonlinear Stability Criteria for the HMF Model
    • Authors: Mohammed Lemou; Ana Maria Luz; Florian Méhats
      Pages: 353 - 380
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1077-4
      Issue No: Vol. 224, No. 2 (2017)
  • Estimates for the Large Time Behavior of the Landau Equation in the
           Coulomb Case
    • Authors: Kleber Carrapatoso; Laurent Desvillettes; Lingbing He
      Pages: 381 - 420
      Abstract: Abstract This work deals with the large time behaviour of the spatially homogeneous Landau equation with Coulomb potential. Firstly, we obtain a bound from below of the entropy dissipation D(f) by weighted relative Fisher information of f with respect to the associated Maxwellian distribution, which leads to a variant of Cercignani’s conjecture thanks to a logarithmic Sobolev inequality. Secondly, we prove the propagation of polynomial and stretched exponential moments with an at-most linearly growing in-time rate. As an application of these estimates, we show the convergence of any (H- or weak) solution to the Landau equation with Coulomb potential to the associated Maxwellian equilibrium with an explicitly computable rate, assuming initial data with finite mass, energy, entropy and some higher L 1-moment. More precisely, if the initial data have some (large enough) polynomial L 1-moment, then we obtain an algebraic decay. If the initial data have a stretched exponential L 1-moment, then we recover a stretched exponential decay.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1078-3
      Issue No: Vol. 224, No. 2 (2017)
  • Steady Prandtl Boundary Layer Expansions Over a Rotating Disk
    • Authors: Sameer Iyer
      Pages: 421 - 469
      Abstract: Abstract This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier-Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid limit. In so doing, we develop a new set of function spaces and prove several embedding theorems which capture the interaction between the Prandtl scaling and the geometry of our domain.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1080-9
      Issue No: Vol. 224, No. 2 (2017)
  • Non-uniqueness and h-Principle for Hölder-Continuous Weak Solutions
           of the Euler Equations
    • Authors: Sara Daneri; László Székelyhidi
      Pages: 471 - 514
      Abstract: Abstract In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. We prove that the set of Hölder \({1/5 - \varepsilon}\) wild initial data is dense in \({L^{2}}\) , where we call an initial datum wild if it admits infinitely many admissible Hölder \({1/5 - \varepsilon}\) weak solutions. We also introduce a new set of stationary flows which we use as a perturbation profile instead of Beltrami flows in order to show that a general form of the h-principle applies to Hölder-continuous weak solutions of the Euler equations. Our result indicates that in a deterministic theory of three dimensional turbulence the Reynolds stress tensor can be arbitrary and need not satisfy any additional closure relation.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1081-8
      Issue No: Vol. 224, No. 2 (2017)
  • On the Motion of Free Interface in Ideal Incompressible MHD
    • Authors: Chengchun Hao
      Pages: 515 - 553
      Abstract: Abstract For the free boundary problem of the plasma–vacuum interface to 3D ideal incompressible magnetohydrodynamics, the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of view and some quantities such as the second fundamental form and the velocity of the free interface are estimated. In the vacuum region, the magnetic fields are described by the div–curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic fields are tangential to the interface, but we do not need any restrictions on the size of the magnetic fields on the free interface. We introduce the “fictitious particle” endowed with a fictitious velocity field in vacuum to reformulate the problem to a fixed boundary problem under the Lagrangian coordinates. The L 2-norms of any order covariant derivatives of the magnetic fields both in vacuum and on the boundaries are bounded in terms of initial data and the second fundamental forms of the free interface and the rigid wall. The estimates of the curl of the electric fields in vacuum are also obtained, which are also indispensable in elliptic estimates.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1082-7
      Issue No: Vol. 224, No. 2 (2017)
  • Zero-Viscosity Limit of the Navier–Stokes Equations in the Analytic
    • Authors: Chao Wang; Yuxi Wang; Zhifei Zhang
      Pages: 555 - 595
      Abstract: Abstract In this paper, we consider the zero-viscosity limit of the Navier–Stokes equations in a half space with non-slip boundary condition. Based on the vorticity formulation and the use of conormal derivative, we develop an energy method to justify the zero-viscosity limit for the analytic data.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1083-6
      Issue No: Vol. 224, No. 2 (2017)
  • Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
    • Authors: Habib Ammari; Pierre Millien; Matias Ruiz; Hai Zhang
      Pages: 597 - 658
      Abstract: Abstract Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is fourfold: (1) to mathematically define the notion of plasmonic resonance and to analyze the shift and broadening of the plasmon resonance with changes in size and shape of the nanoparticles; (2) to study the scattering and absorption enhancements by plasmon resonant nanoparticles and express them in terms of the polarization tensor of the nanoparticle; (3) to derive optimal bounds on the enhancement factors; (4) to show, by analyzing the imaginary part of the Green function, that one can achieve super-resolution and super-focusing using plasmonic nanoparticles. For simplicity, the Helmholtz equation is used to model electromagnetic wave propagation.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1084-5
      Issue No: Vol. 224, No. 2 (2017)
  • Stochastic Allen–Cahn Approximation of the Mean Curvature Flow:
           Large Deviations Upper Bound
    • Authors: Lorenzo Bertini; Paolo Buttà; Adriano Pisante
      Pages: 659 - 707
      Abstract: Abstract Consider the Allen–Cahn equation on the d-dimensional torus, d =  2, 3, in the sharp interface limit. As is well known, the limiting dynamics is described by the motion by mean curvature of the interface between the two stable phases. Here, we analyze a stochastic perturbation of the Allen–Cahn equation and describe its large deviation asymptotics in a joint sharp interface and small noise limit. Relying on previous results on the variational convergence of the action functional, we prove the large deviations upper bound. The corresponding rate function is finite only when there exists a time evolving interface of codimension one between the two stable phases. The zero level set of this rate function is given by the evolution by mean curvature in the sense of Brakke. Finally, the rate function can be written in terms of the sum of two non-negative quantities: the first measures how much the velocity of the interface deviates from its mean curvature, while the second is due to the possible occurrence of nucleation events.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1086-3
      Issue No: Vol. 224, No. 2 (2017)
  • Local Invertibility in Sobolev Spaces with Applications to Nematic
           Elastomers and Magnetoelasticity
    • Authors: Marco Barchiesi; Duvan Henao; Carlos Mora-Corral
      Pages: 743 - 816
      Abstract: Abstract We define a class of deformations in \({W^{1,p}(\Omega,\mathbb{R}^n)}\) , \({p > n-1}\) , with a positive Jacobian, that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality Det = det (that the distributional determinant coincides with the pointwise determinant of the gradient). Maps in this class are shown to satisfy a property of weak monotonicity, and, as a consequence, they enjoy an extra degree of regularity. We also prove that these deformations are locally invertible; moreover, the neighbourhood of invertibility is stable along a weak convergent sequence in \({W^{1,p}}\) , and the sequence of local inverses converges to the local inverse. We use those features to show weak lower semicontinuity of functionals defined in the deformed configuration and functionals involving composition of maps. We apply those results to prove the existence of minimizers in some models for nematic elastomers and magnetoelasticity.
      PubDate: 2017-05-01
      DOI: 10.1007/s00205-017-1088-1
      Issue No: Vol. 224, No. 2 (2017)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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