Existence of Weak Solution of Navier-Stokes-Fourier System with a New Successive Approximation Method

Rabé Bade, Hedia Chaker

Abstract

In This paper we prove the existence of a weak solution of the complete compressible Navier-Stokes system. We follow an previous work where we added an artificial viscosity in the continuity equation and then rewrite the system in hyperbolic and symmetric form. Our study is based on the symmetric hyperbolic theory. We use for this aim a successive approximation in time to show the existence of the hyperbolic system solution and by the fixed point theorem the compacity property of some appropriate sobolev spaces and some established a priori estimates we can pass to several limits to prove our result. As state law, we use the Stiffened gas law.

Keywords

Fluid dynamic, Weak solution, Iterative procedures

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