Periodic Perturbations of a Composite Wave of Two Viscous Shocks for 1-d Full Compressible Navier--Stokes Equations
Periodic Perturbations of a Composite Wave of Two Viscous Shocks for 1-d Full Compressible Navier--Stokes Equations
复制标题
一维全可压缩纳维-斯托克斯方程的两个粘性激波复合波的周期扰动
DOI：
10.1137/21m1421489
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发表时间：
2022
影响因子：
2
通讯作者：
Yuan Yuan
中科院分区：
文献类型：
--
作者：
Qian Yuan;Yuan Yuan
本文研究了一维可压缩Navier-Stokes方程在空间周期扰动下两个粘性激波复合波的渐近稳定性。证明了随着时间的增加，解以一个位移逼近背景复合波，当两个激波的周期扰动和强度都很小时，位移可以唯一确定.证明的关键是构造一个合适的证明，使得反导数方法有效。
This paper is concerned with the asymptotic stability of a composite wave of two viscous shocks under spatially periodic perturbations for the 1-D full compressible Navier-Stokes equations. It is proved that as time increases, the solution approaches the background composite wave with a shift for each shock, where the shifts can be uniquely determined if both the periodic perturbations and strengths of two shocks are small. The key of the proof is to construct a suitable ansatz such that the anti-derivative method works.