TY - JOUR

T1 - Global existence of weak solutions for compressible Navier-Stokese quations

T2 - Thermodynamically unstable pressure and anisotropic viscous stress tensor

AU - Bresch, Didier

AU - Jabin, Pierre Emmanuel

N1 - Funding Information:
Keywords: Compressible Navier–Stokes , global-weak solutions, transport equation, propagation of regularity, non-monotone pressure laws, anisotropic viscous stress, vacuum state, non-local terms AMS Classification: Primary: 35Q30, 35D30, 54D30, 42B37, 35Q86, 92B05. D. Bresch is partially supported by the ANR-13-BS01-0003-01 project DYFI-COLTI. P.-E. Jabin is partially supported by NSF Grant 1312142 and by NSF Grant RNMS (Ki-Net) 1107444. ©c 2018 Department of Mathematics, Princeton University.

PY - 2018

Y1 - 2018

N2 - We prove global existence of appropriate weak solutions for the com- pressible Navier-Stokese quations for amoregeneral stress tensor than those previously covered by P.-L. Lionsand E. Feireisl's theory. Morepre- cisely we focus on more general pressure laws that are not thermodynami- callystable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events(virial pressure law), geophysical flows(eddy viscosity)or biological situations (anisotropy).

AB - We prove global existence of appropriate weak solutions for the com- pressible Navier-Stokese quations for amoregeneral stress tensor than those previously covered by P.-L. Lionsand E. Feireisl's theory. Morepre- cisely we focus on more general pressure laws that are not thermodynami- callystable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events(virial pressure law), geophysical flows(eddy viscosity)or biological situations (anisotropy).

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U2 - 10.4007/ANNALS.2018.188.2.4

DO - 10.4007/ANNALS.2018.188.2.4

M3 - Article

AN - SCOPUS:85055500353

VL - 188

SP - 577

EP - 684

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 2

ER -