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.

中文翻译：

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正压 Navier-Stokes 系统激波大扰动的收缩特性

本文致力于构建一个伪范数，其中正压 Navier-Stokes 方程的小冲击剖面具有收缩特性。这种收缩特性适用于正压 Navier-Stokes 方程的任何大型一维弱解。它意味着一种与粘度强度无关的稳定条件。该证明基于相对熵方法，并且让人想起作者在双曲线情况下首先引入的收缩的概念。