Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system
Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system
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DOI：
10.4171/jems/1018
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发表时间：
2017-12
影响因子：
2.6
通讯作者：
Moon-Jin Kang;A. Vasseur
中科院分区：
文献类型：
--
作者：
Moon-Jin Kang;A. Vasseur
本文致力于构造一个伪范数，使正压Navier-Stokes方程的小激波廓线具有收缩性质。这种收缩性质在正压Navier-Stokes方程的任何大的一维弱解类中成立。这意味着一个稳定性条件，这是独立的强度的粘度。证明是基于相对熵的方法，并让人想起的概念，第一次介绍了作者在双曲的情况下，a-收缩。
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.