可压缩Navier-Stokes方程粘性激波和稀疏波组成的复合波的长时间渐近稳定性（王益）

2023-06-12 | 撰稿： | 浏览:

2023-06-12 | 撰稿： | 浏览:

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 Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas. The same authors introduced it officially as an open problem in 1992 in Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas and it was again described as very challenging open problem in 2018 in the survey paper Waves in compressible fluids: viscous shock, rarefaction, and contact waves. 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 the a-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. **Publication:**Advances in Mathematics, Volume 419, 15 April 2023, 108963 **Author:***Moon-Jin Kang,*Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea;*Alexis F. Vasseur,*Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA;*Yi Wang,*Institute of Applied Mathematics, AMSS, CAS, Beijing 100190, PR China/School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China **Email:** wangyi@amss.ac.cn

地址 北京市海淀区中关村东路55号 思源楼6-7层 南楼5-6、8层 邮编：100190 电子邮箱：iam@amss.ac.cn

@2000-2022 京ICP备05058656号-1

@2000-2022 京ICP备05058656号-1