English

Generalized solutions to models of compressible viscous fluids

Analysis of PDEs 2020-01-01 v1

Abstract

We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides with the strong solution as long as the latter exists (weak-strong uniqueness) and they solve the problem in the classical sense as soon as they are smooth (compatibility). We consider general models of compressible viscous fluids with non-linear viscosity tensor and non-homogeneous boundary conditions, for which the problem of existence of global-in-time weak/strong solutions is largely open.

Keywords

Cite

@article{arxiv.1912.12896,
  title  = {Generalized solutions to models of compressible viscous fluids},
  author = {Anna Abbatiello and Eduard Feireisl and Antonin Novotny},
  journal= {arXiv preprint arXiv:1912.12896},
  year   = {2020}
}