Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations

D. Bresch; P. -E. Jabin

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arXiv · 1602.04373

Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations

D. Bresch·P. -E. Jabin

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Abstract

This short paper is an introduction of the memoir recently written by the two authors (see [D.Bresch., P.--E. Jabin, arXiv:1507.04629, (2015)]) which concerns the resolution of two longstanding problems: Global existence of weak solutions for compressible Navier-Stokes equations with thermodynamically unstable pressure and with anisotropic stress tensor. We focus here on a Stokes-like system which can for instance model flows in a compressible tissue in biology or in a compressible porous media in petroleum engineering. This allows us to explain, on a simpler but still relevant and important system, the tools recently introduced by the authors and to discuss the important results that have been obtained on the compressible Navier--Stokes equations. It is finally a real pleasure to dedicate this paper to G. Metivier for his 65's Birthday. The article will appear in the corresponding special issue, Springer INdAM-Series, Eds F. Colombini, D. Del Santos, D. Lannes (2016).

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BibTeX RIS

D. Bresch, P. -E. Jabin. 2016-02-13. Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations. https://arxiv.org/abs/1602.04373

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