Vanishing dissipation limit for the Navier–Stokes–Fourier system

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 $\Omega \subset R^3$, on the boundary of which the velocity field satisfies the complete slip boundary conditions.

Keywords

inviscid limit, compressible fluid, Navier–Stokes–Fourier system

2010 Mathematics Subject Classification

35B25, 35Q30, 35Q79

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Published 12 August 2016