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March  2003, 2(1): 107-137. doi: 10.3934/cpaa.2003.2.107

$L^1$ 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, France
2. 

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

Received  April 2002 Revised  September 2002 Published  December 2002

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: large amplitude, conservation law, compressible fluids, continuous dependence, entropy solution, Euler equations, large total variation., uniqueness.
Mathematics Subject Classification: 35L65, 76L05, 35L, 76.
Citation: Paola Goatin, Philippe G. LeFloch. $L^1$ continuous dependence for the Euler equations of compressible fluids dynamics. Communications on Pure and Applied Analysis, 2003, 2 (1) : 107-137. doi: 10.3934/cpaa.2003.2.107
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