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PHYSICS (580 journals)                  1 2 3 | Last

Showing 1 - 200 of 741 Journals sorted alphabetically
Acta Acustica united with Acustica     Full-text available via subscription   (Followers: 5)
Acta Mechanica     Hybrid Journal   (Followers: 17)
Acta Scientifica Naturalis     Open Access  
Advanced Composite Materials     Hybrid Journal   (Followers: 58)
Advanced Functional Materials     Hybrid Journal   (Followers: 43)
Advanced Materials     Hybrid Journal   (Followers: 199)
Advanced Science Focus     Free   (Followers: 3)
Advanced Structural and Chemical Imaging     Open Access   (Followers: 2)
Advances in Condensed Matter Physics     Open Access   (Followers: 6)
Advances in Exploration Geophysics     Full-text available via subscription   (Followers: 2)
Advances in Geophysics     Full-text available via subscription   (Followers: 5)
Advances in High Energy Physics     Open Access   (Followers: 16)
Advances in Imaging and Electron Physics     Full-text available via subscription   (Followers: 2)
Advances in Materials Physics and Chemistry     Open Access   (Followers: 15)
Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (Followers: 11)
Advances in OptoElectronics     Open Access   (Followers: 3)
Advances In Physics     Hybrid Journal   (Followers: 10)
Advances in Physics Theories and Applications     Open Access   (Followers: 11)
Advances in Remote Sensing     Open Access   (Followers: 29)
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: 3)
American Journal of Signal Processing     Open Access   (Followers: 8)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 2)
Annalen der Physik     Hybrid Journal   (Followers: 4)
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  
Annual Reports on NMR Spectroscopy     Full-text available via subscription   (Followers: 2)
Annual Review of Analytical Chemistry     Full-text available via subscription   (Followers: 9)
Annual Review of Condensed Matter Physics     Full-text available via subscription   (Followers: 1)
Annual Review of Materials Research     Full-text available via subscription   (Followers: 5)
APL Materials     Open Access   (Followers: 10)
Applied Composite Materials     Hybrid Journal   (Followers: 41)
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: 10)
Applied Radiation and Isotopes     Hybrid Journal   (Followers: 6)
Applied Remote Sensing Journal     Open Access   (Followers: 29)
Applied Spectroscopy     Full-text available via subscription   (Followers: 24)
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  
Astronomy & Geophysics     Hybrid Journal   (Followers: 8)
Astronomy and Astrophysics Review     Hybrid Journal   (Followers: 5)
Astrophysical Journal Supplement Series     Full-text available via subscription   (Followers: 4)
Atoms     Open Access  
Attention, Perception & Psychophysics     Full-text available via subscription   (Followers: 7)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 6)
Axioms     Open Access  
Bangladesh Journal of Medical Physics     Open Access  
Bauphysik     Hybrid Journal   (Followers: 2)
Biomaterials     Hybrid Journal   (Followers: 38)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 15)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 24)
Biophysical Reviews     Hybrid Journal  
Biophysical Reviews and Letters     Hybrid Journal   (Followers: 2)
BMC Biophysics     Open Access   (Followers: 5)
Boson Journal of Modern Physics     Open Access  
Brazilian Journal of Physics     Hybrid Journal  
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 9)
Bulletin of Materials Science     Open Access   (Followers: 41)
Bulletin of the Atomic Scientists     Full-text available via subscription   (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: 1)
Case Studies in Nondestructive Testing and Evaluation     Open Access   (Followers: 4)
Cells     Open Access   (Followers: 1)
CERN courier. International journal of high energy physics     Free   (Followers: 6)
Chemical Physics of Solid Surfaces     Full-text available via subscription  
Chinese Journal of Astronomy and Astrophysics     Full-text available via subscription   (Followers: 3)
Chinese Journal of Chemical Physics     Hybrid Journal   (Followers: 1)
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 Computational Physics     Full-text available via subscription   (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: 1)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 155)
Composites Part B : Engineering     Hybrid Journal   (Followers: 194)
Computational Astrophysics and Cosmology     Open Access  
Computational Condensed Matter     Open Access  
Computational Materials Science     Hybrid Journal   (Followers: 20)
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: 2)
Contemporary Concepts of Condensed Matter Science     Full-text available via subscription  
Contemporary Physics     Hybrid Journal   (Followers: 16)
Continuum Mechanics and Thermodynamics     Hybrid Journal   (Followers: 6)
Contributions to Plasma Physics     Hybrid Journal   (Followers: 2)
COSPAR Colloquia Series     Full-text available via subscription   (Followers: 5)
Cryogenics     Hybrid Journal   (Followers: 43)
Current Applied Physics     Full-text available via subscription   (Followers: 4)
Current Science     Open Access   (Followers: 31)
Diamond and Related Materials     Hybrid Journal   (Followers: 12)
Doklady Physics     Hybrid Journal   (Followers: 1)
Dynamical Properties of Solids     Full-text available via subscription  
ECS Journal of Solid State Science and Technology     Full-text available via subscription   (Followers: 3)
EDUSAINS     Open Access  
Egyptian Journal of Remote Sensing and Space Science     Open Access   (Followers: 18)
EJNMMI Physics     Open Access  
Electrospinning     Open Access  
Embedded Systems Letters, IEEE     Hybrid Journal   (Followers: 38)
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: 3)
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: 6)
European Journal of Physics Education     Open Access   (Followers: 3)
European Physical Journal - Applied Physics     Full-text available via subscription   (Followers: 7)
European Physical Journal C     Hybrid Journal   (Followers: 1)
Europhysics News     Open Access  
Experimental Mechanics     Hybrid Journal   (Followers: 21)
Experimental Methods in the Physical Sciences     Full-text available via subscription  
Experimental Techniques     Hybrid Journal   (Followers: 56)
Exploration Geophysics     Hybrid Journal   (Followers: 3)
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: 9)
Fortschritte der Physik/Progress of Physics     Hybrid Journal  
Frontiers in Physics     Open Access   (Followers: 5)
Frontiers of Materials Science     Hybrid Journal   (Followers: 3)
Frontiers of Physics     Hybrid Journal   (Followers: 2)
Fusion Engineering and Design     Hybrid Journal   (Followers: 9)
Geochemistry, Geophysics, Geosystems     Full-text available via subscription   (Followers: 25)
Geografiska Annaler, Series A: Physical Geography     Hybrid Journal   (Followers: 3)
Geophysical Research Letters     Full-text available via subscription   (Followers: 79)
Geoscience and Remote Sensing, IEEE Transactions on     Hybrid Journal   (Followers: 58)
Glass Physics and Chemistry     Hybrid Journal   (Followers: 3)
Global Journal of Physics     Open Access   (Followers: 1)
Granular Matter     Hybrid Journal   (Followers: 1)
Graphs and Combinatorics     Hybrid Journal   (Followers: 6)
Gravitation and Cosmology     Hybrid Journal   (Followers: 2)
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: 2)
Handbook of Thermal Analysis and Calorimetry     Full-text available via subscription  
Haptics, IEEE Transactions on     Hybrid Journal   (Followers: 3)
Heat Transfer - Asian Research     Hybrid Journal   (Followers: 9)
High Energy Density Physics     Hybrid Journal   (Followers: 2)
High Pressure Research: An International Journal     Hybrid Journal   (Followers: 4)
IEEE Journal of Quantum Electronics     Hybrid Journal   (Followers: 20)
IEEE Signal Processing Magazine     Full-text available via subscription   (Followers: 59)
IET Optoelectronics     Hybrid Journal   (Followers: 1)
Il Colle di Galileo     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: 5)
Indian Journal of Pure & Applied Physics (IJPAP)     Open Access   (Followers: 13)
Indian Journal of Radio & Space Physics (IJRSP)     Open Access   (Followers: 16)
Industrial Electronics, IEEE Transactions on     Hybrid Journal   (Followers: 25)
Industry Applications, IEEE Transactions on     Hybrid Journal   (Followers: 5)
Infinite Dimensional Analysis, Quantum Probability and Related Topics     Hybrid Journal  
InfraMatics     Open Access  
Infrared Physics & Technology     Hybrid Journal  
Intelligent Transportation Systems Magazine, IEEE     Full-text available via subscription   (Followers: 7)
Intermetallics     Hybrid Journal   (Followers: 23)
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: 2)
International Journal of Abrasive Technology     Hybrid Journal   (Followers: 2)
International Journal of Aeroacoustics     Full-text available via subscription   (Followers: 27)
International Journal of Applied Electronics in Physics & Robotics     Open Access   (Followers: 4)
International Journal of Astronomy and Astrophysics     Open Access   (Followers: 7)
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: 35)
International Journal of Fracture     Hybrid Journal   (Followers: 11)
International Journal of Geometric Methods in Modern Physics     Hybrid Journal   (Followers: 1)
International Journal of Geophysics     Open Access   (Followers: 5)
International Journal of Heat and Fluid Flow     Hybrid Journal   (Followers: 31)
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: 15)
International Journal of Material Forming     Hybrid Journal  
International Journal of Materials and Product Technology     Hybrid Journal   (Followers: 4)
International Journal of Mechanical Sciences     Hybrid Journal   (Followers: 11)
International Journal of Mechanics and Materials in Design     Hybrid Journal   (Followers: 5)

        1 2 3 | Last

Journal Cover Archive for Rational Mechanics and Analysis
  [SJR: 3.472]   [H-I: 57]   [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  [2334 journals]
  • A Density Problem for Sobolev Spaces on Planar Domains
    • Authors: Pekka Koskela; Yi Ru-Ya Zhang
      Pages: 1 - 14
      Abstract: We prove that for a bounded, simply connected domain \({\Omega \subset {\mathbb{R}^{2}}}\) , the Sobolev space \({W^{1,\,\infty}(\Omega)}\) is dense in \({W^{1,\,p}(\Omega)}\) for any \({1\leqq p < \infty}\) . Moreover, we show that if \({\Omega}\) is Jordan, then \({C^{\infty}({\mathbb{R}^{2}})}\) is dense in \({W^{1,\,p}(\Omega)}\) for \({1\leqq p < \infty}\) .
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-0994-y
      Issue No: Vol. 222, No. 1 (2016)
  • Zero Viscosity Limit for Analytic Solutions of the Primitive Equations
    • Authors: Igor Kukavica; Maria Carmela Lombardo; Marco Sammartino
      Pages: 15 - 45
      Abstract: The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be \({O(\sqrt{\nu})}\) . The main assumption is spatial analyticity of the initial datum.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-0995-x
      Issue No: Vol. 222, No. 1 (2016)
  • On an Elliptic Equation Arising from Composite Materials
    • Authors: Hongjie Dong; Hong Zhang
      Pages: 47 - 89
      Abstract: In this paper, we derive an interior Schauder estimate for the divergence form elliptic equation $$D_i (a(x)D_iu) = D_i f_i$$ in \({\mathbb{R}^2}\) ,where \({a(x)}\) and \({f_i (x)}\) are piecewise Hölder continuous in a domain containing two touching balls as subdomains. When \({f_i \equiv 0}\) and a is piecewise constant, we prove that u is piecewise smoothwith bounded derivatives.This completely answers a question raised by Li andVogelius (Arch Ration Mech Anal 153(2):91–151, 2000) in dimension 2.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-0996-9
      Issue No: Vol. 222, No. 1 (2016)
  • Partial Regularity for Holonomic Minimisers of Quasiconvex Functionals
    • Authors: Christopher P. Hopper
      Pages: 91 - 141
      Abstract: We prove partial regularity for local minimisers of certain strictly quasiconvex integral functionals, over a class of Sobolev mappings into a compact Riemannian manifold, to which such mappings are said to be holonomically constrained. Our approach uses the lifting of Sobolev mappings to the universal covering space, the connectedness of the covering space, an application of Ekeland’s variational principle and a certain tangential \({\mathbb{A}}\) -harmonic approximation lemma obtained directly via a Lipschitz approximation argument. This allows regularity to be established directly on the level of the gradient. Several applications to variational problems in condensed matter physics with broken symmetries are also discussed, in particular those concerning the superfluidity of liquid helium-3 and nematic liquid crystals.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-0997-8
      Issue No: Vol. 222, No. 1 (2016)
  • Stability of Traveling Waves of Nonlinear Schrödinger Equation with
           Nonzero Condition at Infinity
    • Authors: Zhiwu Lin; Zhengping Wang; Chongchun Zeng
      Pages: 143 - 212
      Abstract: We study the stability of traveling waves of the nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models for this are the Gross–Pitaevskii (GP) equation and the cubic-quintic equation. First, under a non-degeneracy condition we prove a sharp instability criterion for 3D traveling waves of (GP), which had been conjectured in the physical literature. This result is also extended for general nonlinearity and higher dimensions, including 4D (GP) and 3D cubic-quintic equations. Second, for cubic-quintic type nonlinearity, we construct slow traveling waves and prove their nonlinear instability in any dimension. For dimension two, the non-degeneracy condition is also proved for these slow traveling waves. For general traveling waves without vortices (that is nonvanishing) and with general nonlinearity in any dimension, we find a sharp condition for linear instability. Third, we prove that any 2D traveling wave of (GP) is transversally unstable, and we find the sharp interval of unstable transversal wave numbers. Near unstable traveling waves of all of the above cases, we construct unstable and stable invariant manifolds.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-0998-7
      Issue No: Vol. 222, No. 1 (2016)
  • Splash Singularities for the One-Phase Muskat Problem in Stable Regimes
    • Authors: Angel Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo
      Pages: 213 - 243
      Abstract: In this paper we show the existence in finite time of splash singularities for the one-phase Muskat problem.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-0999-6
      Issue No: Vol. 222, No. 1 (2016)
  • Partially Strong Transparency Conditions and a Singular Localization
           Method In Geometric Optics
    • Authors: Yong Lu; Zhifei Zhang
      Pages: 245 - 283
      Abstract: This paper focuses on the stability analysis of WKB approximate solutions in geometric optics with the absence of strong transparency conditions under the terminology of Joly, Métivier and Rauch. We introduce a compatible condition and a singular localization method which allows us to prove the stability of WKB solutions over long time intervals. This compatible condition is weaker than the strong transparency condition. The singular localization method allows us to do delicate analysis near resonances. As an application, we show the long time approximation of Klein–Gordon equations by Schrödinger equations in the non-relativistic limit regime.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-1000-4
      Issue No: Vol. 222, No. 1 (2016)
  • On Bifurcating Time-Periodic Flow of a Navier-Stokes Liquid Past a
    • Authors: Giovanni P. Galdi
      Pages: 285 - 315
      Abstract: We provide general sufficient conditions for the existence and uniqueness of branching out of a time-periodic family of solutions from steady-state solutions to the two-dimensional Navier-Stokes equations in the exterior of a cylinder. By separating the time-independent averaged component of the velocity field from its oscillatory one, we show that the problem can be formulated as a coupled elliptic-parabolic nonlinear system in appropriate and distinct function spaces, with the property that the relevant linearized operators become Fredholm of index 0. In this functional setting, the notorious difficulty of 0 being in the essential spectrum entirely disappears and, in fact, it is even meaningless. Our approach is different and, we believe, more natural and simpler than those proposed by previous authors discussing similar questions. Moreover, the latter all fail, when applied to the problem studied here.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-1001-3
      Issue No: Vol. 222, No. 1 (2016)
  • Global Weak Solutions for Kolmogorov–Vicsek Type Equations with
           Orientational Interactions
    • Authors: Irene M. Gamba; Moon-Jin Kang
      Pages: 317 - 342
      Abstract: We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov–Vicsek models that can be considered as non-local, non-linear, Fokker–Planck type equations describing the dynamics of individuals with orientational interactions. This model is derived from the discrete Couzin–Vicsek algorithm as mean-field limit (Bolley et al., Appl Math Lett, 25:339–343, 2012; Degond et al., Math Models Methods Appl Sci 18:1193–1215, 2008), which governs the interactions of stochastic agents moving with a velocity of constant magnitude, that is, the corresponding velocity space for these types of Kolmogorov–Vicsek models is the unit sphere. Our analysis for L p estimates and compactness properties take advantage of the orientational interaction property, meaning that the velocity space is a compact manifold.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-1002-2
      Issue No: Vol. 222, No. 1 (2016)
  • Criteria on Contractions for Entropic Discontinuities of Systems of
           Conservation Laws
    • Authors: Moon-Jin Kang; Alexis F. Vasseur
      Pages: 343 - 391
      Abstract: We study the contraction properties (up to shift) for admissible Rankine–Hugoniot discontinuities of \({n\times n}\) systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in (Serre and Vasseur, J l’Ecole Polytech 1, 2014), using the spatially inhomogeneous pseudo-distance introduced in (Vasseur, Contemp Math AMS, 2013). Our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems, including the Euler system. Moreover, we introduce necessary conditions for contraction, specifically targeted for intermediate shocks. As an application, we show that intermediate shocks of the two-dimensional isentropic magnetohydrodynamics do not verify any of our contraction properties. We also investigate the contraction properties, for contact discontinuities of the Euler system, for a certain range of contraction weights. None of the results involve any smallness condition on the initial perturbation or on the size of the shock.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-1003-1
      Issue No: Vol. 222, No. 1 (2016)
  • Bounded Correctors in Almost Periodic Homogenization
    • Authors: Scott Armstrong; Antoine Gloria; Tuomo Kuusi
      Pages: 393 - 426
      Abstract: We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies the almost periodic assumption and includes (but is not restricted to) the class of smooth, quasiperiodic coefficient fields which satisfy a Diophantine-type condition previously considered by Kozlov (Mat Sb (N.S), 107(149):199–217, 1978). The proof is based on a quantitative ergodic theorem for almost periodic functions combined with the new regularity theory recently introduced by Armstrong and Shen (Pure Appl Math, 2016) for equations with almost periodic coefficients. This yields control on spatial averages of the gradient of the corrector, which is converted into estimates on the size of the corrector itself via a multiscale Poincaré-type inequality.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-1004-0
      Issue No: Vol. 222, No. 1 (2016)
  • Minimizers of the Landau–de Gennes Energy Around a Spherical Colloid
    • Authors: Stan Alama; Lia Bronsard; Xavier Lamy
      Pages: 427 - 450
      Abstract: We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The nematic is assumed to occupy the exterior of a ball B r0, and satisfy homeotropic weak anchoring at the surface of the colloid and approach a uniform uniaxial state as \({ x \to\infty}\) . We study the minimizers in two different limiting regimes: for balls which are small \({r_0\ll L^{\frac12}}\) compared to the characteristic length scale \({L^{\frac 12}}\) , and for large balls, \({r_0\gg L^{\frac12}}\) . The relationship between the radius and the anchoring strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a “Saturn ring” defect for relatively strong anchoring, corresponding to an exchange of eigenvalues of the Q-tensor. In the limit of very large balls we obtain an axisymmetric minimizer of the Oseen–Frank energy, and a dipole configuration with exactly one point defect is obtained.
      PubDate: 2016-10-01
      DOI: 10.1007/s00205-016-1005-z
      Issue No: Vol. 222, No. 1 (2016)
  • Global Strong Well-Posedness of the Three Dimensional Primitive Equations
           in $${L^p}$$ L p -Spaces
    • Authors: Matthias Hieber; Takahito Kashiwabara
      Pages: 1077 - 1115
      Abstract: In this article, an \({L^p}\) -approach to the primitive equations is developed. In particular, it is shown that the three dimensional primitive equations admit a unique, global strong solution for all initial data \({a \in [X_p,D(A_p)]_{1/p}}\) provided \({p \in [6/5,\infty)}\) . To this end, the hydrostatic Stokes operator \({A_p}\) defined on \({X_p}\) , the subspace of \({L^p}\) associated with the hydrostatic Helmholtz projection, is introduced and investigated. Choosing \({p}\) large, one obtains global well-posedness of the primitive equations for strong solutions for initial data \({a}\) having less differentiability properties than \({H^1}\) , hereby generalizing in particular a result by Cao and Titi (Ann Math 166:245–267, 2007) to the case of non-smooth initial data.
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0979-x
      Issue No: Vol. 221, No. 3 (2016)
  • Impermeability Through a Perforated Domain for the Incompressible two
           dimensional Euler Equations
    • Authors: Christophe Lacave; Nader Masmoudi
      Pages: 1117 - 1160
      Abstract: We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size \({\varepsilon}\) separated by distances \({d_{\varepsilon}}\) and the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit of \({\frac{d_{\varepsilon}}\varepsilon}\) when \({\varepsilon}\) goes to zero. If \({\frac{d_{\varepsilon}}\varepsilon \to \infty}\) , then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary, \({\frac{d_{\varepsilon}}\varepsilon \to 0}\) , then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit of \({\frac{d_{\varepsilon}}{\varepsilon^{2+\frac1\gamma}}}\) where \({\gamma \in (0,\infty]}\) is related to the geometry of the lateral boundaries of the obstacles. If \({\frac{d_{\varepsilon}}{\varepsilon^{2+\frac1\gamma}} \to \infty}\) , then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal to \({\varepsilon^{3}}\) for balls.
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0980-4
      Issue No: Vol. 221, No. 3 (2016)
  • The Blow Up Method for Brakke Flows: Networks Near Triple Junctions
    • Authors: Yoshihiro Tonegawa; Neshan Wickramasekera
      Pages: 1161 - 1222
      Abstract: We introduce a parabolic blow-up method to study the asymptotic behavior of a Brakke flow of planar networks (that is a 1-dimensional Brakke flow in a two dimensional region) weakly close in a space-time region to a static multiplicity 1 triple junction J. We show that such a network flow is regular in a smaller space-time region, in the sense that it consists of three curves coming smoothly together at a single point at 120 \({^{\circ}}\) angles, staying smoothly close to J and moving smoothly. Using this result and White’s stratification theorem, we deduce that whenever a Brakke flow of networks in a space-time region \({{\mathcal {R}}}\) has no static tangent flow with density \({{\geqq}2}\) , there exists a closed subset \({{\Sigma \subset {\mathcal {R}}}}\) of parabolic Hausdorff dimension at most 1 such that the flow is classical in \({{\mathcal {R}}\backslash\Sigma}\) , that is near every point in \({{\mathcal {R}}\backslash\Sigma}\) , the flow, if non-empty, consists of either an embedded curve moving smoothly or three embedded curves meeting smoothly at a single point at 120 \({^{\circ}}\) angles and moving smoothly. In particular, such a flow is classical at all times except for a closed set of times of ordinary Hausdorff dimension at most \({\frac{1}{2}}\) .
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0981-3
      Issue No: Vol. 221, No. 3 (2016)
  • On the Regularity Set and Angular Integrability for the
           Navier–Stokes Equation
    • Authors: Piero D’Ancona; Renato Lucà
      Pages: 1255 - 1284
      Abstract: We investigate the size of the regular set for suitable weak solutions of the Navier–Stokes equation, in the sense of Caffarelli–Kohn–Nirenberg (Commun Pure Appl Math 35:771–831, 1982). We consider initial data in weighted Lebesgue spaces with mixed radial-angular integrability, and we prove that the regular set increases if the data have higher angular integrability, invading the whole half space \({\{t > 0\}}\) in an appropriate limit. In particular, we obtain that if the \({L^{2}}\) norm with weight \({ x ^{-\frac12}}\) of the data tends to 0, the regular set invades \({\{t > 0\}}\) ; this result improves Theorem D of Caffarelli et al. (Commun Pure Appl Math 35:771–831, 1982).
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0982-2
      Issue No: Vol. 221, No. 3 (2016)
  • Global Well-Posedness and Decay Rates of Strong Solutions to a
           Non-Conservative Compressible Two-Fluid Model
    • Authors: Steinar Evje; Wenjun Wang; Huanyao Wen
      Pages: 1285 - 1316
      Abstract: In this paper, we consider a compressible two-fluid model with constant viscosity coefficients and unequal pressure functions \({P^+\neq P^-}\) . As mentioned in the seminal work by Bresch, Desjardins, et al. (Arch Rational Mech Anal 196:599–629, 2010) for the compressible two-fluid model, where \({P^+=P^-}\) (common pressure) is used and capillarity effects are accounted for in terms of a third-order derivative of density, the case of constant viscosity coefficients cannot be handled in their settings. Besides, their analysis relies on a special choice for the density-dependent viscosity [refer also to another reference (Commun Math Phys 309:737–755, 2012) by Bresch, Huang and Li for a study of the same model in one dimension but without capillarity effects]. In this work, we obtain the global solution and its optimal decay rate (in time) with constant viscosity coefficients and some smallness assumptions. In particular, capillary pressure is taken into account in the sense that \({\Delta P=P^+ - P^-=f\neq 0}\) where the difference function \({f}\) is assumed to be a strictly decreasing function near the equilibrium relative to the fluid corresponding to \({P^-}\) . This assumption plays an key role in the analysis and appears to have an essential stabilization effect on the model in question.
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0984-0
      Issue No: Vol. 221, No. 3 (2016)
  • Linear Inviscid Damping for Monotone Shear Flows in a Finite Periodic
           Channel, Boundary Effects, Blow-up and Critical Sobolev Regularity
    • Authors: Christian Zillinger
      Pages: 1449 - 1509
      Abstract: In a previous article (Zillinger, Linear inviscid damping for monotone shear flows, 2014), we have established linear inviscid damping for a large class of monotone shear flows in a finite periodic channel and have further shown that boundary effects asymptotically lead to the formation of singularities of derivatives of the solution as \({t \rightarrow \infty}\) . As the main results of this article, we provide a detailed description of the singularity formation and establish stability in all sub-critical fractional Sobolev spaces and blow-up in all super-critical spaces. Furthermore, we discuss the implications of the blow-up to the problem of nonlinear inviscid damping in a finite periodic channel, where high regularity would be essential to control nonlinear effects.
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0991-1
      Issue No: Vol. 221, No. 3 (2016)
  • Stochastic Homogenization of Nonconvex Unbounded Integral Functionals with
           Convex Growth
    • Authors: Mitia Duerinckx; Antoine Gloria
      Pages: 1511 - 1584
      Abstract: We consider the well-trodden ground of the problem of the homogenization of random integral functionals. When the integrand has standard growth conditions, the qualitative theory is well-understood. When it comes to unbounded functionals, that is, when the domain of the integrand is not the whole space and may depend on the space-variable, there is no satisfactory theory. In this contribution we develop a complete qualitative stochastic homogenization theory for nonconvex unbounded functionals with convex growth. We first prove that if the integrand is convex and has p-growth from below (with p > d, the dimension), then it admits homogenization regardless of growth conditions from above. This result, that crucially relies on the existence and sublinearity at infinity of correctors, is also new in the periodic case. In the case of nonconvex integrands, we prove that a similar homogenization result holds provided that the nonconvex integrand admits a two-sided estimate by a convex integrand (the domain of which may depend on the space variable) that itself admits homogenization. This result is of interest to the rigorous derivation of rubber elasticity from polymer physics, which involves the stochastic homogenization of such unbounded functionals.
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0992-0
      Issue No: Vol. 221, No. 3 (2016)
  • Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi
    • Authors: Songting Luo; Hung V. Tran; Yifeng Yu
      Pages: 1585 - 1617
      Abstract: We look at the effective Hamiltonian \({\overline{H}}\) associated with the Hamiltonian \({H(p,x)=H(p)+V(x)}\) in the periodic homogenization theory. Our central goal is to understand the relation between \({V}\) and \({\overline{H}}\) . We formulate some inverse problems concerning this relation. Such types of inverse problems are, in general, very challenging. In this paper, we discuss several special cases in both convex and nonconvex settings.
      PubDate: 2016-09-01
      DOI: 10.1007/s00205-016-0993-z
      Issue No: Vol. 221, No. 3 (2016)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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