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PHYSICS (584 journals)                  1 2 3 | Last

Showing 1 - 200 of 741 Journals sorted alphabetically
Acta Acustica united with Acustica     Full-text available via subscription   (Followers: 8)
Acta Mechanica     Hybrid Journal   (Followers: 20)
Acta Scientifica Naturalis     Open Access   (Followers: 2)
Advanced Composite Materials     Hybrid Journal   (Followers: 68)
Advanced Functional Materials     Hybrid Journal   (Followers: 51)
Advanced Materials     Hybrid Journal   (Followers: 283)
Advanced Science Focus     Free   (Followers: 4)
Advanced Structural and Chemical Imaging     Open Access   (Followers: 2)
Advanced Studies in Theoretical Physics     Open Access  
Advances in Condensed Matter Physics     Open Access   (Followers: 9)
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: 19)
Advances in Imaging and Electron Physics     Full-text available via subscription   (Followers: 2)
Advances in Materials Physics and Chemistry     Open Access   (Followers: 24)
Advances in Natural Sciences: Nanoscience and Nanotechnology     Open Access   (Followers: 30)
Advances in OptoElectronics     Open Access   (Followers: 5)
Advances In Physics     Hybrid Journal   (Followers: 20)
Advances in Physics : X     Open Access  
Advances in Physics Theories and Applications     Open Access   (Followers: 13)
Advances in Remote Sensing     Open Access   (Followers: 43)
AIP Advances     Open Access   (Followers: 8)
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: 11)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Annalen der Physik     Hybrid Journal   (Followers: 5)
Annales Geophysicae (ANGEO)     Open Access   (Followers: 19)
Annales Henri Poincaré     Hybrid Journal   (Followers: 3)
Annales UMCS, Physica     Open Access  
Annals of Nuclear Medicine     Hybrid Journal   (Followers: 4)
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: 4)
Annual Review of Analytical Chemistry     Full-text available via subscription   (Followers: 11)
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: 13)
Applied Composite Materials     Hybrid Journal   (Followers: 48)
Applied Physics A     Hybrid Journal   (Followers: 8)
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: 7)
Applied Spectroscopy     Full-text available via subscription   (Followers: 22)
Applied Spectroscopy Reviews     Hybrid Journal   (Followers: 4)
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: 23)
Astrophysical Journal Supplement Series     Full-text available via subscription   (Followers: 9)
Atoms     Open Access   (Followers: 1)
Attention, Perception & Psychophysics     Full-text available via subscription   (Followers: 13)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 9)
Axioms     Open Access   (Followers: 1)
Bangladesh Journal of Medical Physics     Open Access  
Bauphysik     Hybrid Journal   (Followers: 2)
Berkala Fisika Indonesia     Open Access  
Biomaterials     Hybrid Journal   (Followers: 46)
Biomedical Engineering, IEEE Reviews in     Full-text available via subscription   (Followers: 18)
Biomedical Engineering, IEEE Transactions on     Hybrid Journal   (Followers: 34)
Biophysical Reviews     Hybrid Journal   (Followers: 1)
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: 43)
Bulletin of the Atomic Scientists     Hybrid Journal   (Followers: 4)
Bulletin of the Lebedev Physics Institute     Hybrid Journal   (Followers: 1)
Bulletin of the Russian Academy of Sciences: Physics     Hybrid Journal   (Followers: 2)
Caderno Brasileiro de Ensino de Física     Open Access  
Canadian Journal of Physics     Hybrid Journal   (Followers: 14)
Case Studies in Nondestructive Testing and Evaluation     Open Access   (Followers: 12)
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: 15)
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   (Followers: 1)
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: 2)
Communications in Numerical Methods in Engineering     Hybrid Journal   (Followers: 2)
Communications in Theoretical Physics     Full-text available via subscription   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 206)
Composites Part B : Engineering     Hybrid Journal   (Followers: 258)
Computational Astrophysics and Cosmology     Open Access   (Followers: 1)
Computational Condensed Matter     Open Access  
Computational Materials Science     Hybrid Journal   (Followers: 22)
Computational Mathematics and Mathematical Physics     Hybrid Journal   (Followers: 3)
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)
Condensed Matter     Open Access  
Contemporary Concepts of Condensed Matter Science     Full-text available via subscription  
Contemporary Physics     Hybrid Journal   (Followers: 26)
Continuum Mechanics and Thermodynamics     Hybrid Journal   (Followers: 8)
Contributions to Plasma Physics     Hybrid Journal   (Followers: 4)
COSPAR Colloquia Series     Full-text available via subscription   (Followers: 8)
Cryogenics     Hybrid Journal   (Followers: 53)
Current Applied Physics     Full-text available via subscription   (Followers: 4)
Current Science     Open Access   (Followers: 68)
Diagnostic and Interventional Imaging     Full-text available via subscription  
Diamond and Related Materials     Hybrid Journal   (Followers: 12)
Doklady Physics     Hybrid Journal   (Followers: 1)
Dynamical Properties of Solids     Full-text available via subscription  
East European Journal of Physics     Open Access  
ECS Journal of Solid State Science and Technology     Hybrid Journal   (Followers: 6)
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: 45)
Energy Procedia     Open Access   (Followers: 2)
Engineering Failure Analysis     Hybrid Journal   (Followers: 67)
Engineering Fracture Mechanics     Hybrid Journal   (Followers: 24)
Environmental Fluid Mechanics     Hybrid Journal   (Followers: 6)
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: 18)
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: 14)
Fortschritte der Physik/Progress of Physics     Hybrid Journal  
Frontiers in Physics     Open Access   (Followers: 6)
Frontiers of Materials Science     Hybrid Journal   (Followers: 4)
Frontiers of Physics     Hybrid Journal   (Followers: 2)
Fusion Engineering and Design     Hybrid Journal   (Followers: 10)
Geochemistry, Geophysics, Geosystems     Full-text available via subscription   (Followers: 32)
Geografiska Annaler, Series A : Physical Geography     Hybrid Journal   (Followers: 3)
Geophysical Research Letters     Full-text available via subscription   (Followers: 144)
Geoscience and Remote Sensing, IEEE Transactions on     Hybrid Journal   (Followers: 182)
Glass Physics and Chemistry     Hybrid Journal   (Followers: 4)
Granular Matter     Hybrid Journal   (Followers: 1)
Graphs and Combinatorics     Hybrid Journal   (Followers: 7)
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: 4)
Handbook of Thermal Analysis and Calorimetry     Full-text available via subscription   (Followers: 1)
Haptics, IEEE Transactions on     Hybrid Journal   (Followers: 4)
Heat Transfer - Asian Research     Hybrid Journal   (Followers: 12)
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: 22)
IEEE Signal Processing Magazine     Full-text available via subscription   (Followers: 75)
IET Optoelectronics     Hybrid Journal   (Followers: 1)
Il Colle di Galileo     Open Access  
Image Analysis & Stereology     Open Access  
Imaging Science Journal     Hybrid Journal   (Followers: 3)
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: 41)
Industrial Electronics, IEEE Transactions on     Hybrid Journal   (Followers: 46)
Industry Applications, IEEE Transactions on     Hybrid Journal   (Followers: 15)
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: 10)
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: 5)
International Journal for Computational Methods in Engineering Science and Mechanics     Hybrid Journal   (Followers: 12)
International Journal for Ion Mobility Spectrometry     Hybrid Journal   (Followers: 1)
International Journal for Simulation and Multidisciplinary Design Optimization     Open Access   (Followers: 4)
International Journal of Abrasive Technology     Hybrid Journal   (Followers: 2)
International Journal of Aeroacoustics     Hybrid Journal   (Followers: 36)
International Journal of Applied Electronics in Physics & Robotics     Open Access   (Followers: 4)
International Journal of Astronomy and Astrophysics     Open Access   (Followers: 24)
International Journal of Computational Materials Science and Surface Engineering     Hybrid Journal   (Followers: 7)
International Journal of Damage Mechanics     Hybrid Journal   (Followers: 5)
International Journal of Fatigue     Hybrid Journal   (Followers: 37)
International Journal of Fracture     Hybrid Journal   (Followers: 13)
International Journal of Geometric Methods in Modern Physics     Hybrid Journal   (Followers: 2)
International Journal of Heat and Fluid Flow     Hybrid Journal   (Followers: 35)
International Journal of Low Radiation     Hybrid Journal   (Followers: 1)
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  [2351 journals]
  • Freeform Lens Design for Scattering Data with General Radiant Fields
    • Authors: Cristian E. Gutiérrez; Ahmad Sabra
      Pages: 341 - 399
      Abstract: We show the existence of a lens, when its lower face is given, such that it refracts radiation emanating from a planar source, with a given field of directions, into the far field that preserves a given distribution of energies. Conditions are shown under which the lens obtained is physically realizable. It is shown that the upper face of the lens satisfies a pde of Monge-Ampère type.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1196-y
      Issue No: Vol. 228, No. 2 (2018)
  • An Obstacle Problem for Conical Deformations of Thin Elastic Sheets
    • Authors: Alessio Figalli; Connor Mooney
      Pages: 401 - 429
      Abstract: A developable cone (“d-cone”) is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance \({\varepsilon}\) . Starting from a nonlinear model depending on the thickness h > 0 of the sheet, we prove a \({\Gamma}\) -convergence result as \({h \rightarrow 0}\) to a fourth-order obstacle problem for curves in \({\mathbb{S}^2}\) . We then describe the exact shape of minimizers of the limit problem when \({\varepsilon}\) is small. In particular, we rigorously justify previous results in the physics literature.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1195-z
      Issue No: Vol. 228, No. 2 (2018)
  • Three-Dimensional Steady Supersonic Euler Flow Past a Concave Cornered
           Wedge with Lower Pressure at the Downstream
    • Authors: Aifang Qu; Wei Xiang
      Pages: 431 - 476
      Abstract: In this paper, we study the stability of the three-dimensional jet created by a supersonic flow past a concave cornered wedge with the lower pressure at the downstream. The gas beyond the jet boundary is assumed to be static. It can be formulated as a nonlinear hyperbolic free boundary problem in a cornered domain with two characteristic free boundaries of different types: one is the rarefaction wave, while the other one is the contact discontinuity, which can be either a vortex sheet or an entropy wave. A more delicate argument is developed to establish the existence and stability of the square jet structure under the perturbation of the supersonic incoming flow and the pressure at the downstream. The methods and techniques developed here are also helpful for other problems involving similar difficulties.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1197-x
      Issue No: Vol. 228, No. 2 (2018)
  • Two-Phase Anisotropic Free Boundary Problems and Applications to the
           Bellman Equation in 2D
    • Authors: L. Caffarelli; D. De Silva; O. Savin
      Pages: 477 - 493
      Abstract: We prove Lipschitz continuity of solutions to a class of rather general two-phase anisotropic free boundary problems in 2D and we classify global solutions. As a consequence, we obtain \({C^{2,1}}\) regularity of solutions to the Bellman equation in 2D.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1198-9
      Issue No: Vol. 228, No. 2 (2018)
  • Compressible Fluids Interacting with a Linear-Elastic Shell
    • Authors: Dominic Breit; Sebastian Schwarzacher
      Pages: 495 - 562
      Abstract: We study the Navier–Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter’s elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies \({\gamma > \frac{12}{7}}\) ( \({\gamma >1 }\) in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205–255, 2014) on incompressible Navier–Stokes equations.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1199-8
      Issue No: Vol. 228, No. 2 (2018)
  • Gauge Momenta as Casimir Functions of Nonholonomic Systems
    • Authors: Luis C. García-Naranjo; James Montaldi
      Pages: 563 - 602
      Abstract: We consider nonholonomic systems with symmetry possessing a certain type of first integral which is linear in the velocities. We develop a systematic method for modifying the standard nonholonomic almost Poisson structure that describes the dynamics so that these integrals become Casimir functions after reduction. This explains a number of recent results on Hamiltonization of nonholonomic systems, and has consequences for the study of relative equilibria in such systems.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1200-6
      Issue No: Vol. 228, No. 2 (2018)
  • On Stationary Navier–Stokes Flows Around a Rotating Obstacle in
    • Authors: Mitsuo Higaki; Yasunori Maekawa; Yuu Nakahara
      Pages: 603 - 651
      Abstract: We study the two-dimensional stationary Navier–Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1201-5
      Issue No: Vol. 228, No. 2 (2018)
  • Acoustic Scattering from Corners, Edges and Circular Cones
    • Authors: Johannes Elschner; Guanghui Hu
      Pages: 653 - 690
      Abstract: Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions and a planar corner point in two dimensions. The opening angles of cones and edges are allowed to be any number in \({(0,2\pi)\backslash\{\pi\}}\) . We prove that such an obstacle scatters any incoming wave non-trivially (that is, the far field patterns cannot vanish identically), leading to the absence of real non-scattering wavenumbers. Local and global uniqueness results for the inverse problem of recovering the shape of penetrable scatterers are also obtained using a single incoming wave. Our approach relies on the singularity analysis of the inhomogeneous Laplace equation in a cone.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1202-4
      Issue No: Vol. 228, No. 2 (2018)
  • Local Existence of MHD Contact Discontinuities
    • Authors: Alessandro Morando; Yuri Trakhinin; Paola Trebeschi
      Pages: 691 - 742
      Abstract: We prove the local-in-time existence of solutions with a contact discontinuity of the equations of ideal compressible magnetohydrodynamics (MHD) for two dimensional planar flows provided that the Rayleigh–Taylor sign condition \({[\partial p/\partial N] <0 }\) on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity. MHD contact discontinuities are characteristic discontinuities with no flow across the discontinuity for which the pressure, the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump. This paper is a natural completion of our previous analysis (Morando et al. in J Differ Equ 258:2531–2571, 2015) where the well-posedness in Sobolev spaces of the linearized problem was proved under the Rayleigh–Taylor sign condition satisfied at each point of the unperturbed discontinuity. The proof of the resolution of the nonlinear problem given in the present paper follows from a suitable tame a priori estimate in Sobolev spaces for the linearized equations and a Nash–Moser iteration.
      PubDate: 2018-05-01
      DOI: 10.1007/s00205-017-1203-3
      Issue No: Vol. 228, No. 2 (2018)
  • Global Regularity for the Fractional Euler Alignment System
    • Authors: Tam Do; Alexander Kiselev; Lenya Ryzhik; Changhui Tan
      Pages: 1 - 37
      Abstract: We study a pressureless Euler system with a non-linear density-dependent alignment term, originating in the Cucker–Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density dependence is natural: the alignment rate increases in the areas of high density due to species discomfort. The diffusive term has the order of a fractional Laplacian \({(-\partial _{xx})^{\alpha/2}, \alpha \in (0, 1)}\) . The corresponding Burgers equation with a linear dissipation of this type develops shocks in a finite time. We show that the alignment nonlinearity enhances the dissipation, and the solutions are globally regular for all \({\alpha \in (0, 1)}\) . To the best of our knowledge, this is the first example of such regularization due to the non-local nonlinear modulation of dissipation.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1184-2
      Issue No: Vol. 228, No. 1 (2018)
  • Stability of Nonlinear Wave Patterns to the Bipolar
           Vlasov–Poisson–Boltzmann System
    • Authors: Hailiang Li; Yi Wang; Tong Yang; Mingying Zhong
      Pages: 39 - 127
      Abstract: The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov–Poisson–Boltzmann (VPB) system. To this end, motivated by the micro–macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133–179, 2004) and Liu et al. (Physica D 188:178–192, 2004), we first set up a new micro–macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665–725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1185-1
      Issue No: Vol. 228, No. 1 (2018)
  • Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq
    • Authors: Roberto Castelli; Marcio Gameiro; Jean-Philippe Lessard
      Pages: 129 - 157
      Abstract: In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton–Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1186-0
      Issue No: Vol. 228, No. 1 (2018)
  • Parabolic Theory as a High-Dimensional Limit of Elliptic Theory
    • Authors: Blair Davey
      Pages: 159 - 196
      Abstract: The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity theory of parabolic equations and geometric flows. Specifically, we give new proofs of an L 2 Carleman estimate for the heat operator, and the monotonicity formulas for the frequency function associated to the heat operator, the two-phase free boundary problem, the flow of harmonic maps, and the mean curvature flow. The proofs rely only on the underlying elliptic theorems and limiting procedures belonging essentially to probability theory. In particular, each parabolic theorem is proved by taking a high-dimensional limit of the related elliptic result.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1187-z
      Issue No: Vol. 228, No. 1 (2018)
  • Onsager’s Conjecture for the Incompressible Euler Equations in
           Bounded Domains
    • Authors: Claude Bardos; Edriss S. Titi
      Pages: 197 - 207
      Abstract: The goal of this note is to show that, in a bounded domain \({\Omega \subset \mathbb{R}^n}\) , with \({\partial \Omega\in C^2}\) , any weak solution \({(u(x,t),p(x,t))}\) , of the Euler equations of ideal incompressible fluid in \({\Omega\times (0,T) \subset \mathbb{R}^n\times\mathbb{R}_t}\) , with the impermeability boundary condition \({u\cdot \vec n =0}\) on \({\partial\Omega\times(0,T)}\) , is of constant energy on the interval (0,T), provided the velocity field \({u \in L^3((0,T); C^{0,\alpha}(\overline{\Omega}))}\) , with \({\alpha > \frac13.}\)
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1189-x
      Issue No: Vol. 228, No. 1 (2018)
  • Morse Theory and Relative Equilibria in the Planar n -Vortex Problem
    • Authors: Gareth E. Roberts
      Pages: 209 - 236
      Abstract: Morse theoretical ideas are applied to the study of relative equilibria in the planar n-vortex problem. For the case of positive circulations, we prove that the Morse index of a critical point of the Hamiltonian restricted to a level surface of the angular impulse is equal to the number of pairs of real eigenvalues of the corresponding relative equilibrium periodic solution. The Morse inequalities are then used to prove the instability of some families of relative equilibria in the four-vortex problem with two pairs of equal vorticities. We also show that, for positive circulations, relative equilibria cannot accumulate on the collision set.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1190-4
      Issue No: Vol. 228, No. 1 (2018)
  • The Role of the Pressure in the Partial Regularity Theory for Weak
           Solutions of the Navier–Stokes Equations
    • Authors: Diego Chamorro; Pierre-Gilles Lemarié-Rieusset; Kawther Mayoufi
      Pages: 237 - 277
      Abstract: We study the role of the pressure in the partial regularity theory for weak solutions of the Navier–Stokes equations. By introducing the notion of dissipative solutions, due to Duchon and Robert (Nonlinearity 13:249–255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin’s local regularity criterion.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1191-3
      Issue No: Vol. 228, No. 1 (2018)
  • Optimal Micropatterns in 2D Transport Networks and Their Relation to Image
    • Authors: Alessio Brancolini; Carolin Rossmanith; Benedikt Wirth
      Pages: 279 - 308
      Abstract: We consider two different variational models of transport networks: the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford–Shah image inpainting and techniques developed in that field, we show for a two-dimensional situation that both highly non-convex network optimization tasks can be transformed into a convex variational problem, which may be very useful from analytical and numerical perspectives. As applications of the convex formulation, we use it to perform numerical simulations (to our knowledge this is the first numerical treatment of urban planning), and we prove a lower bound for the network cost that matches a known upper bound (in terms of how the cost scales in the model parameters) which helps better understand optimal networks and their minimal costs.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1192-2
      Issue No: Vol. 228, No. 1 (2018)
  • Rectifiability of Line Defects in Liquid Crystals with Variable Degree of
    • Authors: Onur Alper
      Pages: 309 - 339
      Abstract: In [2], Hardt, Lin and the author proved that the defect set of minimizers of the modified Ericksen energy for nematic liquid crystals consists locally of a finite union of isolated points and Hölder continuous curves with finitely many crossings. In this article, we show that each Hölder continuous curve in the defect set is of finite length. Hence, locally, the defect set is rectifiable. For the most part, the proof closely follows the work of De Lellis et al. (Rectifiability and upper minkowski bounds for singularities of harmonic q-valued maps, arXiv:1612.01813, 2016) on harmonic \({\mathcal{Q}}\) -valued maps. The blow-up analysis in Alper et al. (Calc Var Partial Differ Equ 56(5):128, 2017) allows us to simplify the covering arguments in [11] and locally estimate the length of line defects in a geometric fashion.
      PubDate: 2018-04-01
      DOI: 10.1007/s00205-017-1193-1
      Issue No: Vol. 228, No. 1 (2018)
  • The Riemann Problem for the Multidimensional Isentropic System of Gas
           Dynamics is Ill-Posed if It Contains a Shock
    • Authors: Simon Markfelder; Christian Klingenberg
      Pages: 967 - 994
      Abstract: In this paper we consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states, where one state lies in the lower and the other state in the upper half plane. The aim is to investigate whether there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. For some initial states this question has been answered by Feireisl and Kreml (J Hyperbolic Differ Equ 12(3):489–499, 2015), and also Chen and Chen (J Hyperbolic Differ Equ 4(1):105–122, 2007), where there exists a unique entropy solution. For other initial states Chiodaroli and Kreml (Arch Ration Mech Anal 214(3):1019–1049, 2014) and Chiodaroli et al. (Commun Pure Appl Math 68(7):1157–1190, 2015), showed that there are infinitely many entropy solutions. For still other initial states the question on uniqueness remained open and this will be the content of this paper. This paper can be seen as a completion of the aforementioned papers by showing that the solution is non-unique in all cases (except if the solution is smooth).
      PubDate: 2018-03-01
      DOI: 10.1007/s00205-017-1179-z
      Issue No: Vol. 227, No. 3 (2018)
  • Homogeneous Solutions of Stationary Navier–Stokes Equations with
           Isolated Singularities on the Unit Sphere. I. One Singularity
    • Authors: Li Li; YanYan Li; Xukai Yan
      Pages: 1091 - 1163
      Abstract: We classify all (−1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier–Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (−1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (−1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.
      PubDate: 2018-03-01
      DOI: 10.1007/s00205-017-1181-5
      Issue No: Vol. 227, No. 3 (2018)
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