Publisher: Springer-Verlag (Total: 2626 journals)

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Showing 1 - 200 of 2626 Journals sorted alphabetically
3D Printing in Medicine     Open Access   (Followers: 5)
3D Research     Hybrid Journal   (Followers: 21, SJR: 0.222, CiteScore: 1)
4OR: A Quarterly J. of Operations Research     Hybrid Journal   (Followers: 13, SJR: 0.825, CiteScore: 1)
AAPS J.     Hybrid Journal   (Followers: 31, SJR: 1.118, CiteScore: 4)
AAPS PharmSciTech     Hybrid Journal   (Followers: 9, SJR: 0.752, CiteScore: 3)
Abdominal Radiology     Hybrid Journal   (Followers: 22, SJR: 0.866, CiteScore: 2)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4, SJR: 0.439, CiteScore: 0)
aBIOTECH : An Intl. J. on Plant Biotechnology and Agricultural Sciences     Hybrid Journal   (Followers: 2)
Academic Psychiatry     Full-text available via subscription   (Followers: 31, SJR: 0.53, CiteScore: 1)
Academic Questions     Hybrid Journal   (Followers: 9, SJR: 0.106, CiteScore: 0)
Accreditation and Quality Assurance: J. for Quality, Comparability and Reliability in Chemical Measurement     Hybrid Journal   (Followers: 34, SJR: 0.316, CiteScore: 1)
Acoustical Physics     Hybrid Journal   (Followers: 12, SJR: 0.359, CiteScore: 1)
Acoustics Australia     Hybrid Journal   (Followers: 2, SJR: 0.232, CiteScore: 1)
Acta Analytica     Hybrid Journal   (Followers: 7, SJR: 0.367, CiteScore: 0)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1, SJR: 0.675, CiteScore: 1)
Acta Biotheoretica     Hybrid Journal   (Followers: 3, SJR: 0.284, CiteScore: 1)
Acta Diabetologica     Hybrid Journal   (Followers: 19, SJR: 1.587, CiteScore: 3)
Acta Endoscopica     Hybrid Journal   (Followers: 1)
acta ethologica     Hybrid Journal   (Followers: 4, SJR: 0.769, CiteScore: 1)
Acta Geochimica     Hybrid Journal   (Followers: 8, SJR: 0.24, CiteScore: 1)
Acta Geodaetica et Geophysica     Hybrid Journal   (Followers: 3, SJR: 0.305, CiteScore: 1)
Acta Geophysica     Hybrid Journal   (Followers: 11, SJR: 0.312, CiteScore: 1)
Acta Geotechnica     Hybrid Journal   (Followers: 7, SJR: 1.588, CiteScore: 3)
Acta Informatica     Hybrid Journal   (Followers: 5, SJR: 0.517, CiteScore: 1)
Acta Mathematica     Hybrid Journal   (Followers: 13, SJR: 7.066, CiteScore: 3)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2, SJR: 0.452, CiteScore: 1)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6, SJR: 0.379, CiteScore: 1)
Acta Mathematica Vietnamica     Hybrid Journal   (SJR: 0.27, CiteScore: 0)
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal   (SJR: 0.208, CiteScore: 0)
Acta Mechanica     Hybrid Journal   (Followers: 25, SJR: 1.04, CiteScore: 2)
Acta Mechanica Sinica     Hybrid Journal   (Followers: 5, SJR: 0.607, CiteScore: 2)
Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 9, SJR: 0.576, CiteScore: 2)
Acta Meteorologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.638, CiteScore: 1)
Acta Neurochirurgica     Hybrid Journal   (Followers: 7, SJR: 0.822, CiteScore: 2)
Acta Neurologica Belgica     Hybrid Journal   (Followers: 3, SJR: 0.376, CiteScore: 1)
Acta Neuropathologica     Hybrid Journal   (Followers: 5, SJR: 7.589, CiteScore: 12)
Acta Oceanologica Sinica     Hybrid Journal   (Followers: 3, SJR: 0.334, CiteScore: 1)
Acta Physiologiae Plantarum     Hybrid Journal   (Followers: 4, SJR: 0.574, CiteScore: 2)
Acta Politica     Hybrid Journal   (Followers: 19, SJR: 0.605, CiteScore: 1)
Activitas Nervosa Superior     Hybrid Journal   (SJR: 0.147, CiteScore: 0)
Adaptive Human Behavior and Physiology     Hybrid Journal   (Followers: 1)
adhäsion KLEBEN & DICHTEN     Hybrid Journal   (Followers: 9, SJR: 0.103, CiteScore: 0)
ADHD Attention Deficit and Hyperactivity Disorders     Hybrid Journal   (Followers: 28, SJR: 0.72, CiteScore: 2)
Adhesion Adhesives & Sealants     Hybrid Journal   (Followers: 11)
Administration and Policy in Mental Health and Mental Health Services Research     Partially Free   (Followers: 21, SJR: 1.005, CiteScore: 2)
Adolescent Research Review     Hybrid Journal   (Followers: 2)
Adsorption     Hybrid Journal   (Followers: 5, SJR: 0.703, CiteScore: 2)
Advanced Composites and Hybrid Materials     Hybrid Journal  
Advanced Fiber Materials     Full-text available via subscription  
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4, SJR: 0.698, CiteScore: 1)
Advances in Astronautics Science and Technology     Hybrid Journal  
Advances in Atmospheric Sciences     Hybrid Journal   (Followers: 42, SJR: 0.956, CiteScore: 2)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23, SJR: 0.812, CiteScore: 1)
Advances in Contraception     Hybrid Journal   (Followers: 3)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 57, SJR: 1.09, CiteScore: 1)
Advances in Gerontology     Partially Free   (Followers: 8, SJR: 0.144, CiteScore: 0)
Advances in Health Sciences Education     Hybrid Journal   (Followers: 36, SJR: 1.64, CiteScore: 2)
Advances in Manufacturing     Hybrid Journal   (Followers: 5, SJR: 0.475, CiteScore: 2)
Advances in Neurodevelopmental Disorders     Hybrid Journal   (Followers: 2)
Advances in Operator Theory     Hybrid Journal   (Followers: 4)
Advances in Polymer Science     Hybrid Journal   (Followers: 50, SJR: 1.04, CiteScore: 3)
Advances in Therapy     Hybrid Journal   (Followers: 5, SJR: 1.075, CiteScore: 3)
Advances in Traditional Medicine     Hybrid Journal   (Followers: 4)
Adversity and Resilience Science : J. of Research and Practice     Hybrid Journal   (Followers: 3)
Aegean Review of the Law of the Sea and Maritime Law     Hybrid Journal   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2, SJR: 0.517, CiteScore: 1)
Aerobiologia     Hybrid Journal   (Followers: 4, SJR: 0.673, CiteScore: 2)
Aerosol Science and Engineering     Hybrid Journal  
Aerospace Systems     Hybrid Journal   (Followers: 1)
Aerotecnica Missili & Spazio : J. of Aerospace Science, Technologies & Systems     Hybrid Journal  
Aesthetic Plastic Surgery     Hybrid Journal   (Followers: 12, SJR: 0.825, CiteScore: 1)
Affective Science     Hybrid Journal   (Followers: 2)
African Archaeological Review     Hybrid Journal   (Followers: 20, SJR: 0.862, CiteScore: 1)
Afrika Matematika     Hybrid Journal   (Followers: 3, SJR: 0.235, CiteScore: 0)
Ageing Intl.     Hybrid Journal   (Followers: 8, SJR: 0.39, CiteScore: 1)
Aggiornamenti CIO     Hybrid Journal   (Followers: 1)
Aging Clinical and Experimental Research     Hybrid Journal   (Followers: 3, SJR: 0.67, CiteScore: 2)
Agricultural Research     Hybrid Journal   (Followers: 7, SJR: 0.276, CiteScore: 1)
Agriculture and Human Values     Open Access   (Followers: 15, SJR: 1.173, CiteScore: 3)
Agroforestry Systems     Open Access   (Followers: 20, SJR: 0.663, CiteScore: 1)
Agronomy for Sustainable Development     Open Access   (Followers: 19, SJR: 1.864, CiteScore: 6)
AI & Society     Hybrid Journal   (Followers: 9, SJR: 0.227, CiteScore: 1)
AIDS and Behavior     Hybrid Journal   (Followers: 18, SJR: 1.792, CiteScore: 3)
Air Quality, Atmosphere & Health     Hybrid Journal   (Followers: 7, SJR: 0.862, CiteScore: 3)
Akupunktur & Aurikulomedizin     Full-text available via subscription   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 7, SJR: 0.531, CiteScore: 0)
Algebra Universalis     Hybrid Journal   (Followers: 2, SJR: 0.583, CiteScore: 1)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1, SJR: 1.095, CiteScore: 1)
Algorithmica     Hybrid Journal   (Followers: 9, SJR: 0.56, CiteScore: 1)
Allergo J.     Full-text available via subscription   (Followers: 2, SJR: 0.234, CiteScore: 0)
Allergo J. Intl.     Hybrid Journal   (Followers: 2)
Alpine Botany     Hybrid Journal   (Followers: 5, SJR: 1.11, CiteScore: 3)
ALTEX : Alternatives to Animal Experimentation     Open Access   (Followers: 2)
AMBIO     Hybrid Journal   (Followers: 9, SJR: 1.569, CiteScore: 4)
American J. of Cardiovascular Drugs     Hybrid Journal   (Followers: 18, SJR: 0.951, CiteScore: 3)
American J. of Community Psychology     Hybrid Journal   (Followers: 32, SJR: 1.329, CiteScore: 2)
American J. of Criminal Justice     Hybrid Journal   (Followers: 9, SJR: 0.772, CiteScore: 1)
American J. of Cultural Sociology     Hybrid Journal   (Followers: 22, SJR: 0.46, CiteScore: 1)
American J. of Dance Therapy     Hybrid Journal   (Followers: 9, SJR: 0.181, CiteScore: 0)
American J. of Potato Research     Hybrid Journal   (Followers: 3, SJR: 0.611, CiteScore: 1)
American J. of Psychoanalysis     Hybrid Journal   (Followers: 22, SJR: 0.314, CiteScore: 0)
American Sociologist     Hybrid Journal   (Followers: 16, SJR: 0.35, CiteScore: 0)
Amino Acids     Hybrid Journal   (Followers: 7, SJR: 1.135, CiteScore: 3)
AMS Review     Partially Free   (Followers: 4)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 11, SJR: 0.211, CiteScore: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6, SJR: 0.536, CiteScore: 1)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Analysis of Verbal Behavior     Hybrid Journal   (Followers: 6)
Analytical and Bioanalytical Chemistry     Hybrid Journal   (Followers: 32, SJR: 0.978, CiteScore: 3)
Anatomical Science Intl.     Hybrid Journal   (Followers: 3, SJR: 0.367, CiteScore: 1)
Angewandte Schmerztherapie und Palliativmedizin     Hybrid Journal  
Angiogenesis     Hybrid Journal   (Followers: 3, SJR: 2.177, CiteScore: 5)
Animal Cognition     Hybrid Journal   (Followers: 23, SJR: 1.389, CiteScore: 3)
Annales françaises de médecine d'urgence     Hybrid Journal   (Followers: 1, SJR: 0.192, CiteScore: 0)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3, SJR: 1.097, CiteScore: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4, SJR: 0.438, CiteScore: 0)
Annali dell'Universita di Ferrara     Hybrid Journal   (SJR: 0.429, CiteScore: 0)
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1, SJR: 1.197, CiteScore: 1)
Annals of Biomedical Engineering     Hybrid Journal   (Followers: 19, SJR: 1.042, CiteScore: 3)
Annals of Combinatorics     Hybrid Journal   (Followers: 4, SJR: 0.932, CiteScore: 1)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Dyslexia     Hybrid Journal   (Followers: 11, SJR: 0.85, CiteScore: 2)
Annals of Finance     Hybrid Journal   (Followers: 37, SJR: 0.579, CiteScore: 1)
Annals of Forest Science     Hybrid Journal   (Followers: 7, SJR: 0.986, CiteScore: 2)
Annals of Functional Analysis     Hybrid Journal   (Followers: 4)
Annals of Global Analysis and Geometry     Hybrid Journal   (Followers: 1, SJR: 1.228, CiteScore: 1)
Annals of Hematology     Hybrid Journal   (Followers: 15, SJR: 1.043, CiteScore: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 14, SJR: 0.413, CiteScore: 1)
Annals of Microbiology     Hybrid Journal   (Followers: 13, SJR: 0.479, CiteScore: 2)
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 4, SJR: 0.687, CiteScore: 2)
Annals of Operations Research     Hybrid Journal   (Followers: 11, SJR: 0.943, CiteScore: 2)
Annals of Ophthalmology     Hybrid Journal   (Followers: 14)
Annals of PDE     Hybrid Journal   (Followers: 1)
Annals of Regional Science     Hybrid Journal   (Followers: 9, SJR: 0.614, CiteScore: 1)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annals of Solid and Structural Mechanics     Hybrid Journal   (Followers: 11, SJR: 0.239, CiteScore: 1)
Annals of Surgical Oncology     Hybrid Journal   (Followers: 19, SJR: 1.986, CiteScore: 4)
Annals of Telecommunications     Hybrid Journal   (Followers: 8, SJR: 0.223, CiteScore: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1, SJR: 1.495, CiteScore: 1)
Antonie van Leeuwenhoek     Hybrid Journal   (Followers: 5, SJR: 0.834, CiteScore: 2)
Apidologie     Hybrid Journal   (Followers: 5, SJR: 1.22, CiteScore: 3)
APOPTOSIS     Hybrid Journal   (Followers: 9, SJR: 1.424, CiteScore: 4)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3, SJR: 0.294, CiteScore: 1)
Applications of Mathematics     Hybrid Journal   (Followers: 3, SJR: 0.602, CiteScore: 1)
Applied Biochemistry and Biotechnology     Hybrid Journal   (Followers: 42, SJR: 0.571, CiteScore: 2)
Applied Biochemistry and Microbiology     Hybrid Journal   (Followers: 20, SJR: 0.21, CiteScore: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 4, SJR: 0.49, CiteScore: 0)
Applied Composite Materials     Hybrid Journal   (Followers: 53, SJR: 0.58, CiteScore: 2)
Applied Entomology and Zoology     Partially Free   (Followers: 7, SJR: 0.422, CiteScore: 1)
Applied Geomatics     Hybrid Journal   (Followers: 3, SJR: 0.733, CiteScore: 3)
Applied Geophysics     Hybrid Journal   (Followers: 11, SJR: 0.488, CiteScore: 1)
Applied Intelligence     Hybrid Journal   (Followers: 15, SJR: 0.6, CiteScore: 2)
Applied Magnetic Resonance     Hybrid Journal   (Followers: 4, SJR: 0.319, CiteScore: 1)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10, SJR: 0.886, CiteScore: 1)
Applied Mathematics - A J. of Chinese Universities     Hybrid Journal   (Followers: 1, SJR: 0.17, CiteScore: 0)
Applied Mathematics and Mechanics     Hybrid Journal   (Followers: 5, SJR: 0.461, CiteScore: 1)
Applied Microbiology and Biotechnology     Hybrid Journal   (Followers: 71, SJR: 1.182, CiteScore: 4)
Applied Physics A     Hybrid Journal   (Followers: 11, SJR: 0.481, CiteScore: 2)
Applied Physics B: Lasers and Optics     Hybrid Journal   (Followers: 27, SJR: 0.74, CiteScore: 2)
Applied Psychophysiology and Biofeedback     Hybrid Journal   (Followers: 8, SJR: 0.519, CiteScore: 2)
Applied Research in Quality of Life     Hybrid Journal   (Followers: 12, SJR: 0.316, CiteScore: 1)
Applied Solar Energy     Hybrid Journal   (Followers: 21, SJR: 0.225, CiteScore: 0)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6, SJR: 0.542, CiteScore: 1)
Aquaculture Intl.     Hybrid Journal   (Followers: 26, SJR: 0.591, CiteScore: 2)
Aquarium Sciences and Conservation     Hybrid Journal   (Followers: 2)
Aquatic Ecology     Hybrid Journal   (Followers: 38, SJR: 0.656, CiteScore: 2)
Aquatic Geochemistry     Hybrid Journal   (Followers: 3, SJR: 0.591, CiteScore: 1)
Aquatic Sciences     Hybrid Journal   (Followers: 14, SJR: 1.109, CiteScore: 3)
Arabian J. for Science and Engineering     Hybrid Journal   (Followers: 5, SJR: 0.303, CiteScore: 1)
Arabian J. of Geosciences     Hybrid Journal   (Followers: 2, SJR: 0.319, CiteScore: 1)
Archaeological and Anthropological Sciences     Hybrid Journal   (Followers: 24, SJR: 1.052, CiteScore: 2)
Archaeologies     Hybrid Journal   (Followers: 13, SJR: 0.224, CiteScore: 0)
Archiv der Mathematik     Hybrid Journal   (Followers: 1, SJR: 0.725, CiteScore: 1)
Archival Science     Hybrid Journal   (Followers: 70, SJR: 0.745, CiteScore: 2)
Archive for History of Exact Sciences     Hybrid Journal   (Followers: 7, SJR: 0.186, CiteScore: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3, SJR: 0.909, CiteScore: 1)
Archive for Rational Mechanics and Analysis     Hybrid Journal   (Followers: 1, SJR: 3.93, CiteScore: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6, SJR: 0.79, CiteScore: 2)
Archives and Museum Informatics     Hybrid Journal   (Followers: 182, SJR: 0.101, CiteScore: 0)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6, SJR: 1.41, CiteScore: 5)
Archives of Dermatological Research     Hybrid Journal   (Followers: 7, SJR: 1.006, CiteScore: 2)
Archives of Environmental Contamination and Toxicology     Hybrid Journal   (Followers: 14, SJR: 0.773, CiteScore: 2)
Archives of Gynecology and Obstetrics     Hybrid Journal   (Followers: 19, SJR: 0.956, CiteScore: 2)
Archives of Microbiology     Hybrid Journal   (Followers: 10, SJR: 0.644, CiteScore: 2)
Archives of Orthopaedic and Trauma Surgery     Hybrid Journal   (Followers: 10, SJR: 1.146, CiteScore: 2)
Archives of Osteoporosis     Hybrid Journal   (Followers: 2, SJR: 0.71, CiteScore: 2)
Archives of Sexual Behavior     Hybrid Journal   (Followers: 11, SJR: 1.493, CiteScore: 3)
Archives of Toxicology     Hybrid Journal   (Followers: 19, SJR: 1.541, CiteScore: 5)
Archives of Virology     Hybrid Journal   (Followers: 5, SJR: 0.973, CiteScore: 2)
Archives of Women's Mental Health     Hybrid Journal   (Followers: 18, SJR: 1.274, CiteScore: 3)
Archivio di Ortopedia e Reumatologia     Hybrid Journal  
Archivum Immunologiae et Therapiae Experimentalis     Hybrid Journal   (Followers: 2, SJR: 0.946, CiteScore: 3)
ArgoSpine News & J.     Hybrid Journal  
Argumentation     Hybrid Journal   (Followers: 6, SJR: 0.349, CiteScore: 1)
Arid Ecosystems     Hybrid Journal   (Followers: 3, SJR: 0.2, CiteScore: 0)
Arkiv för Matematik     Hybrid Journal   (Followers: 1, SJR: 0.766, CiteScore: 1)
arktos : The J. of Arctic Geosciences     Hybrid Journal  
Arnold Mathematical J.     Hybrid Journal   (Followers: 1, SJR: 0.355, CiteScore: 0)
Arthropod-Plant Interactions     Hybrid Journal   (Followers: 2, SJR: 0.839, CiteScore: 2)
Arthroskopie     Hybrid Journal   (Followers: 1, SJR: 0.131, CiteScore: 0)

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Similar Journals
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Annals of PDE
Number of Followers: 1  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2524-5317 - ISSN (Online) 2199-2576
Published by Springer-Verlag Homepage  [2626 journals]
  • On Pseudospectral Bound for Non-selfadjoint Operators and Its Application
           to Stability of Kolmogorov Flows
    • Abstract: We study the stability of the Kolmogorov flows which are stationary solutions to the two-dimensional Navier–Stokes equations in the presence of the shear external force. We establish the linear stability estimate when the viscosity coefficient \(\nu \) is sufficiently small, where the enhanced dissipation is rigorously verified in the time scale \(O(\nu ^{-\frac{1}{2}})\) for solutions to the linearized problem, which has been numerically conjectured and is much shorter than the usual viscous time scale \(O(\nu ^{-1})\) . Our approach is based on the detailed analysis for the resolvent problem. We also provide the abstract framework which is applicable to the resolvent estimate for the Kolmogorov flows.
      PubDate: 2019-09-09
  • The Linear Stability of the Schwarzschild Solution to Gravitational
           Perturbations in the Generalised Wave Gauge
    • Abstract: Abstract We prove in this paper that the Schwarzschild family of black holes are linearly stable as a family of solutions to the system of equations that result from expressing the Einstein vacuum equations in a generalised wave gauge. In particular we improve on our recent work (Johnson in The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge, arXiv: 1803.04012, 2018) by modifying the generalised wave gauge employed therein so as to establish asymptotic flatness of the associated linearised system. The result thus complements the seminal work (Dafermos et al. in The linear stability of the Schwarzschild solution to gravitational perturbations, arXiv:1601.06467, 2016) of Dafermos–Holzegel–Rodnianski in a similar vein as to how the work (Lindblad and Rodnianski. in Ann Math 171:1401–1477, 2010) of Lindblad–Rodnianski complemented that of Christodoulou–Klainerman (Christodoulou and Klainerman in The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, vol 41. Princeton University Press, Princeton, 1993) in establishing the nonlinear stability of the Minkowski space.
      PubDate: 2019-09-07
  • Splash Singularities for the Free Boundary Navier-Stokes Equations
    • Abstract: Abstract In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Navier-Stokes equations, for which the smoothness of the interface breaks down in finite time into a splash singularity.
      PubDate: 2019-05-11
  • Stability of Vacuum for the Landau Equation with Moderately Soft
    • Abstract: Abstract Consider the spatially inhomogeneous Landau equation with moderately soft potentials (i.e. with \(\gamma \in (-\,2,0)\) ) on the whole space \({\mathbb {R}}^3\) . We prove that if the initial data \(f_{\mathrm {in}}\) are close to the vacuum solution \(f_{\mathrm {vac}} \equiv 0\) in an appropriate norm, then the solution f remains regular globally in time. This is the first stability of vacuum result for a binary collisional model featuring a long-range interaction. Moreover, we prove that the solutions in the near-vacuum regime approach solutions to the linear transport equation as \(t\rightarrow +\,\infty \) . Furthermore, in general, solutions do not approach a traveling global Maxwellian as \(t \rightarrow +\,\infty \) . Our proof relies on robust decay estimates captured using weighted energy estimates and the maximum principle for weighted quantities. Importantly, we also make use of a null structure in the nonlinearity of the Landau equation which suppresses the most slowly-decaying interactions.
      PubDate: 2019-05-08
  • Global Well-Posedness for the Massive Maxwell–Klein–Gordon Equation
           with Small Critical Sobolev Data
    • Abstract: Abstract In this paper we prove global well-posedness and modified scattering for the massive Maxwell–Klein–Gordon equation in the Coulomb gauge on \(\mathbb {R}^{1+d}\) \((d \ge 4)\) for data with small critical Sobolev norm. This extends to the general case \( m^2 > 0 \) the results of Krieger–Sterbenz–Tataru ( \(d=4,5 \) ) and Rodnianski–Tao ( \( d \ge 6 \) ), who considered the case \( m=0\) . We proceed by generalizing the global parametrix construction for the covariant wave operator and the functional framework from the massless case to the Klein–Gordon setting. The equation exhibits a trilinear cancelation structure identified by Machedon–Sterbenz. To treat it one needs sharp \(L^{2}\) null form bounds, which we prove by estimating renormalized solutions in null frames spaces similar to the ones considered by Bejenaru–Herr. To overcome logarithmic divergences we rely on an embedding property of \( \Box ^{-1} \) in conjunction with endpoint Strichartz estimates in Lorentz spaces.
      PubDate: 2019-04-02
  • Loss of Regularity for the Continuity Equation with Non-Lipschitz Velocity
    • Abstract: Abstract We consider the Cauchy problem for the continuity equation in space dimension \({d \ge 2}\) . We construct a divergence-free velocity field uniformly bounded in all Sobolev spaces \(W^{1,p}\) , for \(1 \le p<\infty \) , and a smooth compactly supported initial datum such that the unique solution to the continuity equation with this initial datum and advecting field does not belong to any Sobolev space of positive fractional order at any positive time. We also construct velocity fields in \(W^{r,p}\) , with \(r>1\) , and solutions of the continuity equation with these velocities that exhibit some loss of regularity, as long as the Sobolev space \(W^{r,p}\) does not embed in the space of Lipschitz functions. Our constructions are based on examples of optimal mixers from the companion paper Exponential self-similar mixing by incompressible flows (Alberti et al. in J Am Math Soc 32(2):445–490, 2019), and have been announced in Exponential self-similar mixing and loss of regularity for continuity equations (Alberti et al. in Comptes Rendus Math Acad Sci Paris 352(11):901–906, 2014).
      PubDate: 2019-03-28
  • Well-Posedness of the Prandtl Equations Without Any Structural Assumption
    • Abstract: Abstract We show the local in time well-posedness of the Prandtl equations for data with Gevrey 2 regularity in x and Sobolev regularity in y. The main novelty of our result is that we do not make any assumption on the structure of the initial data: no monotonicity or hypothesis on the critical points. Moreover, our general result is optimal in terms of regularity, in view of the ill-posedness result of Gérard-Varet and Dormy (J Am Math Soc 23(2):591–609, 2010).
      PubDate: 2019-03-19
  • Global Well-Posedness and Large Time Asymptotic Behavior of Classical
           Solutions to the Compressible Navier–Stokes Equations with Vacuum
    • Abstract: Abstract We are concerned with the global well-posedness and large time asymptotic behavior of strong and classical solutions to the Cauchy problem of the Navier–Stokes equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For strong and classical solutions, some a priori decay with rates (in large time) for both the pressure and the spatial gradient of the velocity field are obtained provided that the initial total energy is suitably small. Moreover, by using these key decay rates and some analysis on the expansion rates of the essential support of the density, we establish the global existence and uniqueness of classical solutions (which may be of possibly large oscillations) in two spatial dimensions, provided the smooth initial data are of small total energy. In addition, the initial density can even have compact support. This, in particular, yields the global regularity and uniqueness of the re-normalized weak solutions of Lions–Feireisl to the two-dimensional compressible barotropic flows for all adiabatic number \(\gamma >1\) provided that the initial total energy is small.
      PubDate: 2019-03-15
  • Strong Cosmic Censorship in Spherical Symmetry for Two-Ended
           Asymptotically Flat Initial Data II: The Exterior of the Black Hole Region
    • Abstract: Abstract This is the second and last paper of a two-part series in which we prove the \(C^2\) -formulation of the strong cosmic censorship conjecture for the Einstein–Maxwell–(real)–scalar–field system in spherical symmetry for two-ended asymptotically flat data. In the first paper, we showed that the maximal globally hyperbolic future development of an admissible asymptotially flat Cauchy initial data set is \(C^2\) -future-inextendible provided that an \(L^2\) -averaged (inverse) polynomial lower bound for the derivative of the scalar field holds along each horizon. In this paper, we show that this lower bound is indeed satisfied for solutions arising from a generic set of Cauchy initial data. Roughly speaking, the generic set is open with respect to a (weighted) \(C^1\) topology and is dense with respect to a (weighted) \(C^\infty \) topology. The proof of the theorem is based on extensions of the ideas in our previous work on the linear instability of Reissner–Nordström Cauchy horizon, as well as a new large data asymptotic stability result which gives good decay estimates for the difference of the radiation fields for small perturbations of an arbitrary solution.
      PubDate: 2019-03-06
  • Sharp Asymptotics of the First Exit Point Density
    • Abstract: Abstract We consider the exit event from a metastable state for the overdamped Langevin dynamics \(dX_t = -\nabla f(X_t) dt + \sqrt{h} dB_t\) . Using tools from semiclassical analysis, we prove that, starting from the quasi stationary distribution within the state, the exit event can be modeled using a jump Markov process parametrized with the Eyring–Kramers formula, in the small temperature regime \(h \rightarrow 0\) . We provide in particular sharp asymptotic estimates on the exit distribution which demonstrate the importance of the prefactors in the Eyring–Kramers formula. Numerical experiments indicate that the geometric assumptions we need to perform our analysis are likely to be necessary. These results also hold starting from deterministic initial conditions within the well which are sufficiently low in energy. From a modelling viewpoint, this gives a rigorous justification of the transition state theory and the Eyring–Kramers formula, which are used to relate the overdamped Langevin dynamics (a continuous state space Markov dynamics) to kinetic Monte Carlo or Markov state models (discrete state space Markov dynamics). From a theoretical viewpoint, our analysis paves a new route to study the exit event from a metastable state for a stochastic process.
      PubDate: 2019-03-04
  • Vortex Axisymmetrization, Inviscid Damping, and Vorticity Depletion in the
           Linearized 2D Euler Equations
    • Abstract: Abstract Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the 2D Euler equations. We consider the incompressible 2D Euler equations linearized around a radially symmetric, strictly monotone decreasing vorticity distribution. For sufficiently regular data, we prove the inviscid damping of the \(\theta \) -dependent radial and angular velocity fields with the optimal rates \(\left\ u^r(t)\right\ \lesssim \langle t \rangle ^{-1}\) and \(\left\ u^\theta (t)\right\ \lesssim \langle t \rangle ^{-2}\) in the appropriate radially weighted \(L^2\) spaces. We moreover prove that the vorticity weakly converges back to radial symmetry as \(t \rightarrow \infty \) , a phenomenon known as vortex axisymmetrization in the physics literature, and characterize the dynamics in higher Sobolev spaces. Furthermore, we prove that the \(\theta \) -dependent angular Fourier modes in the vorticity are ejected from the origin as \(t \rightarrow \infty \) , resulting in faster inviscid damping rates than those possible with passive scalar evolution. This non-local effect is called vorticity depletion. Our work appears to be the first to find vorticity depletion relevant for the dynamics of vortices.
      PubDate: 2019-02-12
  • Linear Inviscid Damping and Vorticity Depletion for Shear Flows
    • Abstract: Abstract In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the same decay estimate of the velocity as the monotone shear flows. Moreover, we confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which along with the vorticity mixing leads to the damping for the base flows with stationary streamlines.
      PubDate: 2019-01-25
  • Boundedness and Decay for the Teukolsky Equation on Kerr Spacetimes I: The
           Case $$ a \ll M$$ a ≪ M
    • Abstract: Abstract We prove boundedness and polynomial decay statements for solutions of the spin \(\pm \,2\) Teukolsky equation on a Kerr exterior background with parameters satisfying \( a \ll M\) . The bounds are obtained by introducing generalisations of the higher order quantities P and \({\underline{P}}\) used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters \( a <M\) . As in the Schwarzschild case, these bounds provide the first step in proving the full linear stability of the Kerr metric to gravitational perturbations.
      PubDate: 2019-01-08
  • Smooth Local Solutions to Degenerate Hyperbolic Monge-Ampère
    • Abstract: Abstract In this paper, we prove the existence of smooth solutions near 0 of the degenerate hyperbolic Monge-Ampère equation \(\det (D^2 u) = K(x)h(x,u,Du)\) , where \(K(0)=0\) , \(K\le 0\) , \(h(0,0,0)>0\) . We also assume that, the zero set of small perturbation of \(D_n K\) has a simple structure. For the proof, we first transform the linearized equation into a simple form by a suitable change of variables. Then we proceed to derive a priori estimates for the linearized equation, which is degenerately hyperbolic. Finally we use Nash-Moser iteration to prove the existence of local solutions.
      PubDate: 2019-01-02
  • On the Motion of a Compressible Gravity Water Wave with Vorticity
    • Abstract: Abstract We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary with unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our fluid is not assumed to be irrotational. But the physical sign condition needs to be assumed on the free boundary. We generalize the method used in Lindblad and Luo (Commun Pure Appl Math, 2008) to prove the energy estimates in an unbounded domain up to arbitrary order. In addition to that, the a priori energy estimates are in fact uniform in the sound speed \(\kappa \) . As a consequence, we obtain the convergence of solutions of compressible Euler equations with a free boundary to solutions of the incompressible equations, generalizing the result of Lindblad and Luo (2008) to when you have an unbounded domain. On the other hand, we prove that there are initial data satisfying the compatibility condition in some weighted Sobolev spaces, and this will propagate within a short time interval, which is essential for proving long time existence for slightly compressible irrotational water waves.
      PubDate: 2018-12-11
  • Mean-Field Dynamics for Ginzburg–Landau Vortices with Pinning and
    • Abstract: Abstract We consider the time-dependent 2D Ginzburg–Landau equation in the whole plane with terms modeling impurities and applied currents. The Ginzburg–Landau vortices are then subjected to three forces: their mutual repulsive Coulomb-like interaction, the applied current pushing them in a fixed direction, and the pinning force attracting them towards the impurities. The competition between the three is expected to lead to complicated glassy effects. We rigorously study the limit in which the number of vortices \(N_\varepsilon \) blows up as the inverse Ginzburg–Landau parameter \(\varepsilon \) goes to 0, and we derive via a modulated energy method fluid-like mean-field evolution equations. These results hold for parabolic, conservative, and mixed-flow dynamics in appropriate regimes of \(N_\varepsilon \uparrow \infty \) . Finally, we briefly discuss some natural homogenization questions raised by this study.
      PubDate: 2018-12-10
  • Non-uniqueness for the Transport Equation with Sobolev Vector Fields
    • Abstract: Abstract We construct a large class of examples of non-uniqueness for the linear transport equation and the transport-diffusion equation with divergence-free vector fields in Sobolev spaces \(W^{1, p}\) .
      PubDate: 2018-12-07
  • On the Division Problem for the Wave Maps Equation
    • Abstract: Abstract We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension \(n \geqslant 2\) . We use an adapted version of the atomic space \(U^2\) as the single building block for the iteration space. Our approach to the so-called division problem is modular as it systematically uses two ingredients: atomic bilinear (adjoint) Fourier restriction estimates and an algebra property of the iteration space, both of which can be adapted to other phase functions.
      PubDate: 2018-12-04
  • Scaling and Saturation in Infinite-Dimensional Control Problems with
           Applications to Stochastic Partial Differential Equations
    • Abstract: Abstract We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential equations. We also develop applications concerning associated classes of stochastic partial differential equations (SPDEs). In particular, we study the support properties of probability laws corresponding to these SPDEs as well as provide applications concerning the ergodic and mixing properties of invariant measures for these stochastic systems.
      PubDate: 2018-10-09
  • A Vector Field Approach to Almost-Sharp Decay for the Wave Equation on
           Spherically Symmetric, Stationary Spacetimes
    • Abstract: Abstract We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive a new hierarchy of higher-order weighted energy estimates by employing appropriate commutator vector fields. In cases where an integrated local energy decay estimate holds, like in the case of sub-extremal Reissner–Nordström black holes, this hierarchy leads to almost-sharp global energy and pointwise time-decay estimates with decay rates that go beyond those obtained by the traditional vector field method. Our estimates play a fundamental role in our companion paper where precise late-time asymptotics are obtained for linear scalar fields on such backgrounds.
      PubDate: 2018-09-28
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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