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PHYSICS (578 journals)                  1 2 3 | Last

Showing 1 - 200 of 741 Journals sorted alphabetically
Acta Acustica united with Acustica     Full-text available via subscription   (Followers: 6)
Acta Mechanica     Hybrid Journal   (Followers: 18)
Acta Scientifica Naturalis     Open Access   (Followers: 2)
Advanced Composite Materials     Hybrid Journal   (Followers: 63)
Advanced Functional Materials     Hybrid Journal   (Followers: 48)
Advanced Materials     Hybrid Journal   (Followers: 245)
Advanced Science Focus     Free   (Followers: 3)
Advanced Structural and Chemical Imaging     Open Access   (Followers: 2)
Advances in Condensed Matter Physics     Open Access   (Followers: 8)
Advances in Exploration Geophysics     Full-text available via subscription   (Followers: 3)
Advances in Geophysics     Full-text available via subscription   (Followers: 6)
Advances in High Energy Physics     Open Access   (Followers: 21)
Advances in Imaging and Electron Physics     Full-text available via subscription   (Followers: 2)
Advances in Materials Physics and Chemistry     Open Access   (Followers: 18)
Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (Followers: 28)
Advances in OptoElectronics     Open Access   (Followers: 5)
Advances In Physics     Hybrid Journal   (Followers: 18)
Advances in Physics : X     Open Access  
Advances in Physics Theories and Applications     Open Access   (Followers: 13)
Advances in Remote Sensing     Open Access   (Followers: 35)
AIP Advances     Open Access   (Followers: 9)
AIP Conference Proceedings     Full-text available via subscription   (Followers: 3)
American Journal of Condensed Matter Physics     Open Access   (Followers: 4)
American Journal of Signal Processing     Open Access   (Followers: 10)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Annalen der Physik     Hybrid Journal   (Followers: 5)
Annales Geophysicae (ANGEO)     Open Access   (Followers: 15)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3)
Annales UMCS, Physica     Open Access  
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 5)
Annals of Physics     Hybrid Journal   (Followers: 4)
Annals of West University of Timisoara - Physics     Open Access   (Followers: 1)
Annual Reports on NMR Spectroscopy     Full-text available via subscription   (Followers: 3)
Annual Review of Analytical Chemistry     Full-text available via subscription   (Followers: 9)
Annual Review of Condensed Matter Physics     Full-text available via subscription  
Annual Review of Materials Research     Full-text available via subscription   (Followers: 5)
APL Materials     Open Access   (Followers: 10)
Applied Composite Materials     Hybrid Journal   (Followers: 45)
Applied Physics A     Hybrid Journal   (Followers: 7)
Applied Physics Frontier     Open Access   (Followers: 1)
Applied Physics Letters     Hybrid Journal   (Followers: 33)
Applied Physics Research     Open Access   (Followers: 4)
Applied Physics Reviews     Hybrid Journal   (Followers: 9)
Applied Radiation and Isotopes     Hybrid Journal   (Followers: 7)
Applied Remote Sensing Journal     Open Access   (Followers: 34)
Applied Spectroscopy     Full-text available via subscription   (Followers: 22)
Applied Spectroscopy Reviews     Hybrid Journal   (Followers: 5)
Archive for Rational Mechanics and Analysis     Hybrid Journal  
Asia Pacific Physics Newsletter     Hybrid Journal  
ASTRA Proceedings     Open Access   (Followers: 1)
Astronomy & Geophysics     Hybrid Journal   (Followers: 47)
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 21)
Astrophysical Journal Supplement Series     Full-text available via subscription   (Followers: 8)
Atoms     Open Access   (Followers: 1)
Attention, Perception & Psychophysics     Full-text available via subscription   (Followers: 10)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 7)
Axioms     Open Access  
Bangladesh Journal of Medical Physics     Open Access  
Bauphysik     Hybrid Journal   (Followers: 2)
Berkala Fisika Indonesia     Open Access  
Biomaterials     Hybrid Journal   (Followers: 44)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 16)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 31)
Biophysical Reviews     Hybrid Journal  
Biophysical Reviews and Letters     Hybrid Journal   (Followers: 3)
BMC Biophysics     Open Access   (Followers: 5)
Boson Journal of Modern Physics     Open Access   (Followers: 12)
Brazilian Journal of Physics     Hybrid Journal  
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 10)
Bulletin of Materials Science     Open Access   (Followers: 42)
Bulletin of the Atomic Scientists     Hybrid Journal   (Followers: 3)
Bulletin of the Lebedev Physics Institute     Hybrid Journal   (Followers: 1)
Bulletin of the Russian Academy of Sciences: Physics     Hybrid Journal  
Caderno Brasileiro de Ensino de Física     Open Access  
Canadian Journal of Physics     Full-text available via subscription   (Followers: 14)
Case Studies in Nondestructive Testing and Evaluation     Open Access   (Followers: 9)
Cells     Open Access   (Followers: 2)
CERN courier. International journal of high energy physics     Free   (Followers: 7)
Chemical Physics of Solid Surfaces     Full-text available via subscription  
Chinese Journal of Astronomy and Astrophysics     Full-text available via subscription   (Followers: 13)
Chinese Journal of Chemical Physics     Hybrid Journal   (Followers: 1)
Chinese Journal of Physics     Hybrid Journal  
Chinese Physics B     Full-text available via subscription  
Chinese Physics C     Full-text available via subscription  
Chinese Physics Letters     Full-text available via subscription  
Cogent Physics     Open Access  
Cohesion and Structure     Full-text available via subscription   (Followers: 2)
Colloid Journal     Hybrid Journal   (Followers: 2)
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications in Numerical Methods in Engineering     Hybrid Journal   (Followers: 2)
Communications in Theoretical Physics     Full-text available via subscription   (Followers: 2)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 177)
Composites Part B : Engineering     Hybrid Journal   (Followers: 225)
Computational Astrophysics and Cosmology     Open Access  
Computational Condensed Matter     Open Access  
Computational Materials Science     Hybrid Journal   (Followers: 21)
Computational Mathematics and Mathematical Physics     Hybrid Journal   (Followers: 1)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computer Physics Communications     Hybrid Journal   (Followers: 6)
Contemporary Concepts of Condensed Matter Science     Full-text available via subscription  
Contemporary Physics     Hybrid Journal   (Followers: 27)
Continuum Mechanics and Thermodynamics     Hybrid Journal   (Followers: 6)
Contributions to Plasma Physics     Hybrid Journal   (Followers: 3)
COSPAR Colloquia Series     Full-text available via subscription   (Followers: 7)
Cryogenics     Hybrid Journal   (Followers: 47)
Current Applied Physics     Full-text available via subscription   (Followers: 4)
Current Science     Open Access   (Followers: 48)
Diagnostic and Interventional Imaging     Full-text available via subscription  
Diamond and Related Materials     Hybrid Journal   (Followers: 11)
Doklady Physics     Hybrid Journal   (Followers: 1)
Dynamical Properties of Solids     Full-text available via subscription  
ECS Journal of Solid State Science and Technology     Hybrid Journal   (Followers: 4)
Egyptian Journal of Remote Sensing and Space Science     Open Access   (Followers: 20)
EJNMMI Physics     Open Access  
Electrospinning     Open Access  
Embedded Systems Letters, IEEE     Hybrid Journal   (Followers: 40)
Energy Procedia     Open Access   (Followers: 2)
Engineering Failure Analysis     Hybrid Journal   (Followers: 64)
Engineering Fracture Mechanics     Hybrid Journal   (Followers: 22)
Environmental Fluid Mechanics     Hybrid Journal   (Followers: 5)
EPJ Nonlinear Biomedical Physics     Open Access  
EPJ Quantum Technology     Open Access  
EPJ Techniques and Instrumentation     Full-text available via subscription  
EPJ Web of Conferences     Open Access  
European Journal of Physics     Full-text available via subscription   (Followers: 19)
European Journal of Physics Education     Open Access   (Followers: 3)
European Physical Journal - Applied Physics     Full-text available via subscription   (Followers: 16)
European Physical Journal C     Hybrid Journal   (Followers: 1)
Europhysics News     Open Access  
Experimental Mechanics     Hybrid Journal   (Followers: 22)
Experimental Methods in the Physical Sciences     Full-text available via subscription  
Experimental Techniques     Hybrid Journal   (Followers: 56)
Exploration Geophysics     Hybrid Journal   (Followers: 4)
Few-Body Systems     Hybrid Journal  
Fire and Materials     Hybrid Journal   (Followers: 5)
Flexible Services and Manufacturing Journal     Hybrid Journal   (Followers: 1)
Fluctuation and Noise Letters     Hybrid Journal   (Followers: 1)
Fluid Dynamics     Hybrid Journal   (Followers: 13)
Fortschritte der Physik/Progress of Physics     Hybrid Journal  
Frontiers in Physics     Open Access   (Followers: 6)
Frontiers of Materials Science     Hybrid Journal   (Followers: 3)
Frontiers of Physics     Hybrid Journal   (Followers: 2)
Fusion Engineering and Design     Hybrid Journal   (Followers: 10)
Geochemistry, Geophysics, Geosystems     Full-text available via subscription   (Followers: 26)
Geografiska Annaler, Series A : Physical Geography     Hybrid Journal   (Followers: 3)
Geophysical Research Letters     Full-text available via subscription   (Followers: 107)
Geoscience and Remote Sensing, IEEE Transactions on     Hybrid Journal   (Followers: 130)
Glass Physics and Chemistry     Hybrid Journal   (Followers: 4)
Global Journal of Physics     Open Access   (Followers: 2)
Granular Matter     Hybrid Journal   (Followers: 1)
Graphs and Combinatorics     Hybrid Journal   (Followers: 6)
Gravitation and Cosmology     Hybrid Journal   (Followers: 3)
Handbook of Geophysical Exploration: Seismic Exploration     Full-text available via subscription  
Handbook of Metal Physics     Full-text available via subscription  
Handbook of Surface Science     Full-text available via subscription   (Followers: 3)
Handbook of Thermal Analysis and Calorimetry     Full-text available via subscription   (Followers: 1)
Haptics, IEEE Transactions on     Hybrid Journal   (Followers: 3)
Heat Transfer - Asian Research     Hybrid Journal   (Followers: 11)
High Energy Density Physics     Hybrid Journal   (Followers: 2)
High Pressure Research: An International Journal     Hybrid Journal   (Followers: 3)
IEEE Journal of Quantum Electronics     Hybrid Journal   (Followers: 20)
IEEE Signal Processing Magazine     Full-text available via subscription   (Followers: 62)
IET Optoelectronics     Hybrid Journal   (Followers: 1)
Il Colle di Galileo     Open Access  
Image Analysis & Stereology     Open Access  
Imaging Science Journal     Hybrid Journal   (Followers: 2)
Indian Journal of Biochemistry and Biophysics (IJBB)     Open Access   (Followers: 3)
Indian Journal of Physics     Hybrid Journal   (Followers: 20)
Indian Journal of Pure & Applied Physics (IJPAP)     Open Access   (Followers: 38)
Indian Journal of Radio & Space Physics (IJRSP)     Open Access   (Followers: 35)
Industrial Electronics, IEEE Transactions on     Hybrid Journal   (Followers: 31)
Industry Applications, IEEE Transactions on     Hybrid Journal   (Followers: 7)
Infinite Dimensional Analysis, Quantum Probability and Related Topics     Hybrid Journal  
InfraMatics     Open Access  
Infrared Physics & Technology     Hybrid Journal   (Followers: 11)
Intelligent Transportation Systems Magazine, IEEE     Full-text available via subscription   (Followers: 8)
Intermetallics     Hybrid Journal   (Followers: 22)
International Applied Mechanics     Hybrid Journal   (Followers: 3)
International Geophysics     Full-text available via subscription   (Followers: 3)
International Heat Treatment and Surface Engineering     Hybrid Journal   (Followers: 3)
International Journal for Computational Methods in Engineering Science and Mechanics     Hybrid Journal   (Followers: 10)
International Journal for Ion Mobility Spectrometry     Hybrid Journal   (Followers: 1)
International Journal for Simulation and Multidisciplinary Design Optimization     Open Access   (Followers: 3)
International Journal of Abrasive Technology     Hybrid Journal   (Followers: 2)
International Journal of Aeroacoustics     Hybrid Journal   (Followers: 31)
International Journal of Applied Electronics in Physics & Robotics     Open Access   (Followers: 4)
International Journal of Astronomy and Astrophysics     Open Access   (Followers: 22)
International Journal of Computational Materials Science and Surface Engineering     Hybrid Journal   (Followers: 6)
International Journal of Damage Mechanics     Hybrid Journal   (Followers: 5)
International Journal of Fatigue     Hybrid Journal   (Followers: 33)
International Journal of Fracture     Hybrid Journal   (Followers: 11)
International Journal of Geometric Methods in Modern Physics     Hybrid Journal   (Followers: 2)
International Journal of Geophysics     Open Access   (Followers: 5)
International Journal of Heat and Fluid Flow     Hybrid Journal   (Followers: 32)
International Journal of Low Radiation     Hybrid Journal  
International Journal of Low-Carbon Technologies     Open Access   (Followers: 1)
International Journal of Mass Spectrometry     Hybrid Journal   (Followers: 17)
International Journal of Material Forming     Hybrid Journal   (Followers: 1)

        1 2 3 | Last

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  [2341 journals]
  • Homogenization of the Brush Problem with a Source Term in L 1
    • Authors: Antonio Gaudiello; Olivier Guibé; François Murat
      Pages: 1 - 64
      Abstract: Abstract We consider a domain which has the form of a brush in 3D or the form of a comb in 2D, i.e. an open set which is composed of cylindrical vertical teeth distributed over a fixed basis. All the teeth have a similar fixed height; their cross sections can vary from one tooth to another and are not supposed to be smooth; moreover the teeth can be adjacent, i.e. they can share parts of their boundaries. The diameter of every tooth is supposed to be less than or equal to \({\varepsilon}\) , and the asymptotic volume fraction of the teeth (as \({\varepsilon}\) tends to zero) is supposed to be bounded from below away from zero, but no periodicity is assumed on the distribution of the teeth. In this domain we study the asymptotic behavior (as \({\varepsilon}\) tends to zero) of the solution of a second order elliptic equation with a zeroth order term which is bounded from below away from zero, when the homogeneous Neumann boundary condition is satisfied on the whole of the boundary. First, we revisit the problem where the source term belongs to L 2. This is a classical problem, but our homogenization result takes place in a geometry which is more general that the ones which have been considered before. Moreover we prove a corrector result which is new. Then, we study the case where the source term belongs to L 1. Working in the framework of renormalized solutions and introducing a definition of renormalized solutions for degenerate elliptic equations where only the vertical derivative is involved (such a definition is new), we identify the limit problem and prove a corrector result.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1079-2
      Issue No: Vol. 225, No. 1 (2017)
  • A Measure and Orientation Preserving Homeomorphism with Approximate
           Jacobian Equal −1 Almost Everywhere
    • Authors: Paweł Goldstein; Piotr Hajłasz
      Pages: 65 - 88
      Abstract: Abstract We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit n-dimensional cube onto itself, whose Jacobian is equal to −1 almost everywhere. Moreover, we prove that our homeomorphism can be uniformly approximated by orientation and measure preserving diffeomorphisms.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1085-4
      Issue No: Vol. 225, No. 1 (2017)
  • The Elastic Trefoil is the Doubly Covered Circle
    • Authors: Henryk Gerlach; Philipp Reiter; Heiko von der Mosel
      Pages: 89 - 139
      Abstract: Abstract To describe the behavior of knotted loops of springy wire with an elementary mathematical model we minimize the integral of squared curvature, \({E = \int \varkappa^2}\) , together with a small multiple of ropelength \({\mathcal{R}}\) = length/thickness in order to penalize selfintersection. Our main objective is to characterize all limit configurations of energy minimizers of the total energy \({E_{\vartheta} \equiv E + \vartheta \mathcal{R}}\) as \({\vartheta}\) tends to zero. For short, these limit configurations will be referred to as elastic knots. The elastic unknot turns out to be the once covered circle with squared curvature energy \({(2\pi)^2}\) . For all (non-trivial) knot classes for which the natural lower bound \({(4\pi)^2}\) on E is sharp, the respective elastic knot is the doubly covered circle. We also derive a new characterization of two-bridge torus knots in terms of E, proving that the only knot classes for which the lower bound \({(4\pi)^2}\) on E is sharp are the \({(2,b)}\) -torus knots for odd b with \({ b \ge 3}\) (containing the trefoil knot class). In particular, the elastic trefoil knot is the doubly covered circle.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1100-9
      Issue No: Vol. 225, No. 1 (2017)
  • Global Existence and Asymptotic Behavior of Affine Motion of 3D Ideal
           Fluids Surrounded by Vacuum
    • Authors: Thomas C. Sideris
      Pages: 141 - 176
      Abstract: Abstract The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in \({{\rm GL}^+(3, \mathbb{R})}\) . The evolution of the fluid domain is described by a family of ellipsoids whose diameter grows at a rate proportional to time. Upon rescaling to a fixed diameter, the asymptotic limit of the fluid ellipsoid is determined by a positive semi-definite quadratic form of rank r = 1, 2, or 3, corresponding to the asymptotic degeneration of the ellipsoid along 3−r of its principal axes. In the compressible case, the asymptotic limit has rank r = 3, and asymptotic completeness holds, when the adiabatic index \({\gamma}\) satisfies \({4/3 < \gamma < 2}\) . The number of possible degeneracies, 3−r, increases with the value of the adiabatic index \({\gamma}\) . In the incompressible case, affine motion reduces to geodesic flow in \({{\rm SL}(3, \mathbb{R})}\) with the Euclidean metric. For incompressible affine swirling flow, there is a structural instability. Generically, when the vorticity is nonzero, the domains degenerate along only one axis, but the physical vacuum boundary condition fails over a finite time interval. The rescaled fluid domains of irrotational motion can collapse along two axes.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1106-3
      Issue No: Vol. 225, No. 1 (2017)
  • A Temperature-Dependent Phase-Field Model for Phase Separation and Damage
    • Authors: Christian Heinemann; Christiane Kraus; Elisabetta Rocca; Riccarda Rossi
      Pages: 177 - 247
      Abstract: Abstract In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature concerning phase separation and damage processes in elastic media, in our model we encompass thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More particularly, we prove the existence of “entropic weak solutions”, resorting to a solvability concept first introduced in Feireisl (Comput Math Appl 53:461–490, 2007) in the framework of Fourier–Navier–Stokes systems and then recently employed in Feireisl et al. (Math Methods Appl Sci 32:1345–1369, 2009) and Rocca and Rossi (Math Models Methods Appl Sci 24:1265–1341, 2014) for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1102-7
      Issue No: Vol. 225, No. 1 (2017)
  • A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear
           Elastic Energy in Two Dimensions
    • Authors: Jonathan J. Bevan
      Pages: 249 - 285
      Abstract: Abstract We prove the local Hölder continuity of strong local minimizers of the stored energy functional $$E(u)=\int_{\Omega}\lambda \nabla u ^{2}+h({\rm det} \nabla u)\,{\rm d}x$$ subject to a condition of ‘positive twist’. The latter turns out to be equivalent to requiring that u maps circles to suitably star-shaped sets. The convex function h(s) grows logarithmically as \({s\to 0+}\) , linearly as \({s \to +\infty}\) , and satisfies \({h(s)=+\infty}\) if \({s \leqq 0}\) . These properties encode a constitutive condition which ensures that material does not interpenetrate during a deformation and is one of the principal obstacles to proving the regularity of local or global minimizers. The main innovation is to prove that if a local minimizer has positive twist a.e. on a ball then an Euler-Lagrange type inequality holds and a Caccioppoli inequality can be derived from it. The claimed Hölder continuity then follows by adapting some well-known elliptic regularity theory. We also demonstrate the regularizing effect that the term \({\int_{\Omega} h({\rm det} \nabla u)\,{\rm d}x}\) can have by analysing the regularity of local minimizers in the class of ‘shear maps’. In this setting a more easily verifiable condition than that of positive twist is imposed, with the result that local minimizers are Hölder continuous.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1104-5
      Issue No: Vol. 225, No. 1 (2017)
  • On Stability of Steady Circular Flows in a Two-Dimensional Exterior Disk
    • Authors: Yasunori Maekawa
      Pages: 287 - 374
      Abstract: Abstract We study the stability of some exact stationary solutions to the two-dimensional Navier–Stokes equations in an exterior domain to the unit disk. These stationary solutions are known as a simple model of the flow around a rotating obstacle, while their stability has been open due to the difficulty arising from their spatial decay in a scale-critical order. In this paper we affirmatively settle this problem for small solutions. That is, we will show that if these exact solutions are small enough then they are asymptotically stable with respect to small L 2 perturbations.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1105-4
      Issue No: Vol. 225, No. 1 (2017)
  • Global Well-Posedness of the Boltzmann Equation with Large Amplitude
           Initial Data
    • Authors: Renjun Duan; Feimin Huang; Yong Wang; Tong Yang
      Pages: 375 - 424
      Abstract: Abstract The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new \({L^\infty_xL^1_{v}\cap L^\infty_{x,v}}\) approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted \({L^\infty}\) norm under some smallness condition on the \({L^1_xL^\infty_v}\) norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the \({L^\infty_{x,v}}\) norm with explicit rates of convergence are also studied.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1107-2
      Issue No: Vol. 225, No. 1 (2017)
  • A Derivation of Linearized Griffith Energies from Nonlinear Models
    • Authors: Manuel Friedrich
      Pages: 425 - 467
      Abstract: Abstract We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in a brittle fracture via \({\Gamma}\) -convergence. The convergence is given in terms of rescaled displacement fields measuring the distance of deformations from piecewise rigid motions. The configurations of the limiting model consist of partitions of the material, corresponding piecewise rigid deformations and displacement fields which are defined separately on each component of the cracked body. Apart from the linearized Griffith energy the limiting functional also comprises the segmentation energy, which is necessary to disconnect the parts of the specimen.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1108-1
      Issue No: Vol. 225, No. 1 (2017)
  • Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger
           Equation on $${\mathbb{R}^3}$$ R 3
    • Authors: Rowan Killip; Tadahiro Oh; Oana Pocovnicu; Monica Vişan
      Pages: 469 - 548
      Abstract: Abstract We consider the cubic–quintic nonlinear Schrödinger equation: $$i\partial_t u = -\Delta u - u ^2u + u ^4u.$$ In the first part of the paper, we analyze the one-parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass/energy curve. Additionally, we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one-parameter family of inequalities of Gagliardo–Nirenberg type. Building on this work, in the latter part of the paper we prove that scattering holds for solutions belonging to the region \({{\mathcal{R}}}\) of the mass/energy plane where the virial is positive. We show that this region is partially bounded by solitons also by rescalings of solitons (which are not soliton solutions in their own right). The discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial-based methodology.
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1109-0
      Issue No: Vol. 225, No. 1 (2017)
  • On the Liouville Type Theorems for Self-Similar Solutions to the
           Navier–Stokes Equations
    • Authors: Dongho Chae; Jörg Wolf
      Pages: 549 - 572
      Abstract: Abstract We prove Liouville type theorems for the self-similar solutions to the Navier–Stokes equations. One of our results generalizes the previous ones by Nečas–Ru̇žička–Šverák and Tsai. Using a Liouville type theorem, we also remove a scenario of asymptotically self-similar blow-up for the Navier–Stokes equations with the profile belonging to \({L^{p, \infty} (\mathbb{R}^3)}\) with \({p > \frac{3}{2}}\) .
      PubDate: 2017-07-01
      DOI: 10.1007/s00205-017-1110-7
      Issue No: Vol. 225, No. 1 (2017)
  • 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)
  • 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)
  • 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)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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