Geodesic
Global existence of weak solutions for compressible Navier–Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
Didier Bresch1 ; Pierre--Emmanuel Jabin2
1 Laboratoire de Mathématiques, CNRS UMR5127, Université Grenoble Alpes, Université Savoie Mont Blanc, 73000 Chambéry, France
2 Center for Scientific Computation and Mathematical Modeling (CSCAMM) and Department of Mathematics, University of Maryland, College Park, MD 20742
Annals of mathematics, Tome 188 (2018) no. 2, pp. 577-684

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove global existence of appropriate weak solutions for the compressible Navier–Stokes equations for a more general stress tensor than those previously covered by P.-L.Lions and E. Feireisl’s theory. More precisely we focus on more general pressure laws that are not thermodynamically stable; 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).

DOI : 10.4007/annals.2018.188.2.4

Didier Bresch 1 ; Pierre--Emmanuel Jabin 2

1 Laboratoire de Mathématiques, CNRS UMR5127, Université Grenoble Alpes, Université Savoie Mont Blanc, 73000 Chambéry, France
2 Center for Scientific Computation and Mathematical Modeling (CSCAMM) and Department of Mathematics, University of Maryland, College Park, MD 20742 
@article{10_4007_annals_2018_188_2_4,
     author = {Didier Bresch and Pierre--Emmanuel Jabin},
     title = {Global existence of weak solutions for compressible {Navier{\textendash}Stokes} equations: {Thermodynamically} unstable pressure and anisotropic viscous stress tensor},
     journal = {Annals of mathematics},
     pages = {577--684},
     publisher = {mathdoc},
     volume = {188},
     number = {2},
     year = {2018},
     doi = {10.4007/annals.2018.188.2.4},
     mrnumber = {3862947},
     zbl = {06921187},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.2.4/}
}
TY  - JOUR
AU  - Didier Bresch
AU  - Pierre--Emmanuel Jabin
TI  - Global existence of weak solutions for compressible Navier–Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
JO  - Annals of mathematics
PY  - 2018
SP  - 577
EP  - 684
VL  - 188
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.2.4/
DO  - 10.4007/annals.2018.188.2.4
LA  - en
ID  - 10_4007_annals_2018_188_2_4
ER  - 
%0 Journal Article
%A Didier Bresch
%A Pierre--Emmanuel Jabin
%T Global existence of weak solutions for compressible Navier–Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
%J Annals of mathematics
%D 2018
%P 577-684
%V 188
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.188.2.4/
%R 10.4007/annals.2018.188.2.4
%G en
%F 10_4007_annals_2018_188_2_4
Didier Bresch; Pierre--Emmanuel Jabin. Global existence of weak solutions for compressible Navier–Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor. Annals of mathematics, Tome 188 (2018) no. 2, pp. 577-684. doi: 10.4007/annals.2018.188.2.4

Cité par Sources :