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

Paola Goatin; Philippe G. LeFloch

doi:10.3934/cpaa.2003.2.107

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2003, Volume 2, Issue 1: 107-137. Doi: 10.3934/cpaa.2003.2.107

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

Paola Goatin^1, and
Philippe G. LeFloch^2,

1.
Centre de Mathématiques Appliquées, & Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex
2.
Centre de Mathématiques Appliquées, and Centre National de la Recherche Scientifique, UMR. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex

Received: April 2002

Revised: September 2002

Published: November 2003

Abstract / Introduction Related Papers Cited by

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.

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Mathematics Subject Classification: 35L65, 76L05, 35L, 76N.

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