Global Weak Solutions of PDEs for Compressible Media: A Compactness Criterion to Cover New Physical Situations

DOI10.1007/978-3-319-52042-1_2zbMath1371.35192arXiv1602.04373OpenAlexW3159369941MaRDI QIDQ5275991

Bresch, Didier, Pierre-Emmanuel Jabin

Publication date: 14 July 2017

Published in: Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.04373

zbMATH Keywords

weak solutionsporous mediacompressible Navier-Stokes equationpetroleum engineeringcompressible tissue

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Gas dynamics (general theory) (76N15) Navier-Stokes equations (35Q30) Cell biology (92C37) Weak solutions to PDEs (35D30)

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Cites Work

• Compressible Navier-Stokes equations with a non-monotone pressure law
• An estimate in the spirit of Poincaré's inequality
• Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor
• Compactness for nonlinear continuity equations
• On a nonlinear model for tumor growth: global in time weak solutions
• A viscoelastic model for avascular tumor growth
• Estimates and regularity results for the DiPerna-Lions flow
• Singular limits in thermodynamics of viscous fluids

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