$L^1$ continuous dependence for the Euler equations of compressible fluids dynamics
Paola Goatin - Centre de Mathématiques Appliquées, & 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.
Received: April 2002; Revised: September 2002; Published: December 2002.
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