Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations
Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations
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DOI：
10.1016/j.aim.2023.108963
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发表时间：
2021-04
影响因子：
1.7
通讯作者：
Moon-Jin Kang;A. Vasseur;Yi Wang
中科院分区：
文献类型：
--
作者：
Moon-Jin Kang;A. Vasseur;Yi Wang
本文证明了一维可压缩正压Navier-Stokes方程的粘性激波和稀疏波叠加的复合波的时间渐近稳定性。我们的结果解决了Matsumura和Nishihara在1986年[28]中首次提到的一个长期存在的问题。同一作者在1992年正式将其作为开放问题引入[29]，并在2018年的调查论文中再次将其描述为非常具有挑战性的开放问题[26]。主要的困难是由于不兼容的标准反导数方法，用于研究粘性激波的稳定性，和能量方法用于稀疏的稳定性。而不是反导数的方法，我们的证明使用的是最近开发的两位作者的理论与移位的a-收缩。这种方法是基于能量的，并且可以无缝地处理不同种类的波的叠加。
We prove the time-asymptotic stability of composite waves consisting of the superposition of a viscous shock and a rarefaction for the one-dimensional compressible barotropic Navier-Stokes equations. Our result solves a long-standing problem first mentioned in 1986 by Matsumura and Nishihara in [28]. The same authors introduced it officially as an open problem in 1992 in [29] and it was again described as very challenging open problem in 2018 in the survey paper [26]. The main difficulty is due to the incompatibility of the standard anti-derivative method, used to study the stability of viscous shocks, and the energy method used for the stability of rarefactions. Instead of the anti-derivative method, our proof uses thea-contraction with shifts theory recently developed by two of the authors. This method is energy based, and can seamlessly handle the superposition of waves of different kinds.