Vanishing dissipation limit for the Navier-Stokes-Fourier system

TL;DR

This paper proves that weak solutions of the compressible Navier-Stokes-Fourier system converge to strong solutions of the Euler system as viscosity and heat conductivity vanish, in a bounded domain with slip boundary conditions.

Contribution

It establishes the vanishing dissipation limit for the Navier-Stokes-Fourier system in three dimensions with slip boundary conditions, extending previous results to heat-conducting fluids.

Findings

Weak solutions converge to Euler solutions as dissipation vanishes

Convergence holds on the lifespan of the Euler solution

Results are valid in bounded domains with slip boundary conditions

Abstract

We consider the motion of a compressible, viscous, and heat conducting fluid in the regime of small viscosity and heat conductivity. It is shown that weak solutions of the associated Navier- Stokes-Fourier system converge to a (strong) solution of the Euler system on its life span. The problem is studied in a bounded domain in the three dimensional Euclidean space, on the boundary of which the velocity field satisfies the complete slip boundary conditions.