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

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.