Limit of a Consistent Approximation to the Complete Compressible Euler System

Abstract

The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of the compressible complete Euler system in full space $$ \mathbb {R}^d,\; d=2,3 $$ R d , d = 2 , 3 is a weak solution of the system, then the approximate solutions eventually converge strongly in suitable norms locally under a minimal assumption on the initial data of the approximate solutions. The class of consistent approximate solutions is quite general and includes the vanishing viscosity and heat conductivity limit. In particular, they may not satisfy the minimal principle for entropy.

On oscillatory solutions to the complete Euler system

“…Finally, we report the following result, see Chaudhuri [12], which can be obtained in analogously way as in [24] due to the convexity of pressure.…”