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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer Berlin Heidelberg

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10.1007/bf03045348

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1432-0673

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Weak Solutions of the Navier–Stokes Equations for

Authors: Misha Perepelitsa
Publish Date: 2014/03/27
Volume: 212, Issue: 3, Pages: 709-726
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Abstract

We consider the Navier–Stokes equations for the motion of compressible viscous flows in a halfspace mathbbRn + n =  2  3 with the noslip boundary conditions We prove the existence of a global weak solution when the initial data are close to a static equilibrium The density of the weak solution is uniformly bounded and does not contain a vacuum the velocity is Hölder continuous in x t and the material acceleration is weakly differentiable The weak solutions of this type were introduced by D Hoff in Arch Ration Mech Anal 114115–46 1991 Commun Pure and Appl Math 55111365–1407 2002 for the initialboundary value problem in Omega = mathbbRn and for the problem in Omega = mathbbRn + with the Navier boundary conditions

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  1. Optimal Design in Conductivity Under Locally Constrained Heat Flux
  2. Regularity Issues in the Problem of Fluid Structure Interaction
  3. Negative Eigenvalues of Two-Dimensional Schrödinger Operators
  4. Dobrushin States in the $${\phi^4_1}$$ Model
  5. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  6. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  7. Counterexamples to the Sonic Criterion
  8. Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution
  9. On Nonlinear Stochastic Balance Laws
  10. Generalized Transition Fronts for One-Dimensional Almost Periodic Fisher-KPP Equations
  11. The Gel’fand Problem for the Biharmonic Operator
  12. The Existence Problem for Steiner Networks in Strictly Convex Domains
  13. Stability of Detonation Profiles in the ZND Limit
  14. Uniqueness of Absolute Minimizers for $${L^\infty}$$-Functionals Involving Hamiltonians $${H(x,p)}$$H(x,p)
  15. A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear Elastic Energy in Two Dimensions
  16. Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary
  17. The Toda System and Clustering Interfaces in the Allen–Cahn equation
  18. A Stability Criterion for Two-Fluid Interfaces and Applications
  19. Long-Time Convergence of an Adaptive Biasing Force Method: The Bi-Channel Case
  20. Displacement Convexity and Minimal Fronts at Phase Boundaries
  21. Gradient Bounds for Elliptic Problems Singular at the Boundary
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