Euler system with a polytropic equation of state as a vanishing viscosity limit
Analysis of PDEs
2022-06-22 v1
Abstract
We consider the Euler system of gas dynamics endowed with the incomplete equation of state relating the internal energy to the mass density and the pressure. We show that any sufficiently smooth solution can be recovered as a vanishing viscosity - heat conductivity limit of the Navier--Stokes--Fourier system with a properly defined temperature. The result is unconditional in the case of the Navier type (slip) boundary conditions and extends to the no-slip condition for the velocity under some extra hypotheses of Kato's type concerning the behavior of the fluid in the boundary layer.
Keywords
Cite
@article{arxiv.2109.11294,
title = {Euler system with a polytropic equation of state as a vanishing viscosity limit},
author = {Eduard Feireisl and Christian Klingenberg and Simon Markfelder},
journal= {arXiv preprint arXiv:2109.11294},
year = {2022}
}