Vanishing dissipation limit for the Navier-Stokes-Fourier system

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.