主题：等熵可压NS方程复合波的渐近稳定性

主讲人：中国科学院 王益教授

主持人：经济金沙检测线路js69(科技)有限公司 梁之磊教授

时间：2021年12月2日（周四）10:00-11：00

直播平台及会议ID：腾讯会议， 492911044

主办单位：经济金沙检测线路js69(科技)有限公司 科研处

主讲人简介：

王益，中国科学院数学与系统科学研究院研究员、博士生导师，中国科学院大学教授，入选国家人才计划，主要从事非线性偏微分方程的研究工作，研究兴趣为流体力学方程组的相关数学理论，包括Boltzmann方程的流体动力学极限、流体力学方程组的适定性理论（解的存在唯一性、稳定性和粘性消失极限）等，主要学术论文发表于Arch. Ration. Mech. Anal., Comm. Math. Phys.和SIAM J. Math. Anal.等国际重要刊物上

内容提要：

We talk about our recent result on the time-asymptotic stability of composite waves consisting of the superposition of a viscous shock and a rarefaction for the one-dimensional compressible isentropic Navier-Stokes equation. Our result solves a long-standing problem first mentioned in 1986 by Matsumura and Nishihara in [Japan J. Appl. Math., 1986]. The same authors introduced it officially as an open problem in 1992 in [Comm. Math. Phys., 1992] and it was again described as a very challenging open problem in 2018 in the survey paper [A. Matsumura, Handbook of mathematical analysis in mechanics of viscous fluids, Springer, 2018]. 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 the time-dependent shifts to control the compressibility of viscous shocks in the original perturbation framework for the stability of rarefactions. This method is energy based, and can seamlessly handle the superposition of waves of different kinds.基本波及其它们的耦合形式的稳定性问题是流体力学中关心的基本问题。本报告介绍黏性激波和稀疏波的渐近稳定性问题。 此结果解决了一个公开问题（1986年被首次提出）。证明基于能量估计的办法，主要困难是克服两类反向类型波的耦合。