Measure-valued solutions to the complete Euler system revisited
Abstract
We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier-Stokes-Fourier system. Our main result states that any sequence of weak solutions to the Navier-Stokes-Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.
Cite
@article{arxiv.1710.10751,
title = {Measure-valued solutions to the complete Euler system revisited},
author = {Jan Brezina and Eduard Feireisl},
journal= {arXiv preprint arXiv:1710.10751},
year = {2018}
}