$L^1$ continuous dependence for the Euler equations of compressible fluids dynamics

Pages: 107 - 137, Volume 2, Issue 1, March 2003

doi:10.3934/cpaa.2003.2.107       Abstract        Full Text (266.2K)       Related Articles

Paola Goatin - Centre de Mathématiques Appliquées, & Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France (email)
Philippe G. LeFloch - Centre de Mathématiques Appliquées, and Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France (email)

Abstract: We prove the $L^1$ continuous dependence of entropy solutions for the $2 \times 2$ (isentropic) and the $3\times 3$ (non-isentropic) systems of inviscid fluid dynamics in one-space dimension. We follow the approach developed by the second author for solutions with small total variation to general systems of conservation laws in [11, 14]. For the systems of fluid dynamics under consideration here, our estimates are more precise and we cover entropy solutions with large total variation.

Keywords:  Euler equations, compressible fluids, conservation law, entropy solution, continuous dependence, uniqueness, large amplitude, large total variation.
Mathematics Subject Classification:  35L65, 76L05, 35L, 76N.

Received: April 2002;      Revised: September 2002;      Published: December 2002.