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}
}