报告题目：Time-asymptotic stability of viscous shock and rarefaction waves to the compressible barotropic Navier-Stokes equations

报告人：王益（中国科学院数学与系统科学研究院）

报告时间：2022年5月19日（星期四）13:30-15:00

报告地点：腾讯会议ID：451 962 868

报告摘要：

The talk is concerned with our recent developments on  the time-asymptotic stability of the composite wave of viscous shock and rarefaction to the one-dimensional (1D) compressible barotropic Navier-Stokes equations, which is based on a joint work with Moon-Jin Kang and Alexis Vasseur, and the stability of the planar viscous shock wave to the three-dimensional (3D) barotropic Navier-Stokes equations, which is based on a joint work with Teng Wang. The main points in our proofs are based on the delicate choosing the time-dependent shift functions  for the viscous shock wave and the weight functions in the relative entropy estimates and the using of Poincare-type inequality to overcome the main difficulties due to the compressibility of the viscous shock. Our result for the stability of composite wave of viscous shock and rarefaction to compressible Navier-Stokes equations in 1D case solves an open problem proposed by Matsumura and Nishihara since 1992 and our result for the stability of planar viscous shock wave in 3D case is the first analytic one for multi-dimensional compressible Navier-Stokes equations as far as we know.