偏微分方程系列报告

报告题目: Time-asymptotic stability of composite wave of viscous shock and rarefaction for barotropic Navier-Stokes equations

报告人:  王益 研究员 （中国科学院数学与系统科学研究院）

报告摘要： 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.

报告人简介：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，曾获得国家优秀青年基金并入选第二批国家“万人计划”青年拔尖人才。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、流体力学方程组解的适定性（解的整体存在性、大时间渐进稳定性、粘性消失极限）等。主要论文发表在Arch. Ration. Mech. Anal.、Comm. Math. Phys.和SIAM J. Math. Anal.等国际重要刊物上。

报告时间：2021.11.24 上午10:00

报告地点：腾讯会议 ID：865 385 774，密码：1124