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

Authors

  • Rabé Bade Department of Mathematics et Computer Science
  • Hedia Chaker University of Tunis El-Manar

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3903

Keywords:

Fluid dynamic, Weak solution, Iterative procedures

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.

Author Biography

  • Hedia Chaker, University of Tunis El-Manar
    Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur

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Published

2021-01-31

Issue

Vol. 14 No. 1: (January 2021)

Section

Nonlinear Analysis

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How to Cite

Existence of Weak Solution of Navier-Stokes-Fourier System with a New Successive Approximation Method. (2021). European Journal of Pure and Applied Mathematics, 14(1), 82-111. https://doi.org/10.29020/nybg.ejpam.v14i1.3903