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arXiv · 1712.07348

Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system

Moon-Jin Kang·Alexis Vasseur
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Abstract

This paper is dedicated to the construction of a pseudo-norm, for which small shock profiles of the barotropic Navier-Stokes equation have a contraction property. This contraction property holds in the class of any large 1D weak solutions to the barotropic Navier-Stokes equation. It implies a stability condition which is independent of the strength of the viscosity. The proof is based on the relative entropy method, and is reminiscent to the notion of a-contraction first introduced by the authors in the hyperbolic case.

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Moon-Jin Kang, Alexis Vasseur. 2017-12-20. Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system. https://arxiv.org/abs/1712.07348

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