On a class of generalized solutions to equations describing incompressible viscous fluids
Analysis of PDEs
2019-06-04 v2 Mathematical Physics
math.MP
Abstract
We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by the measure-valued solutions for the inviscid (Euler) system. We show the existence as well as the weak-strong uniqueness property in the class of dissipative solutions. Finally, the dissipative solution enjoying certain extra regularity coincides with a strong solution of the same problem.
Keywords
Cite
@article{arxiv.1905.12732,
title = {On a class of generalized solutions to equations describing incompressible viscous fluids},
author = {A. Abbatiello and E. Feireisl},
journal= {arXiv preprint arXiv:1905.12732},
year = {2019}
}