报告题目：Long-time behavior of weak solutions for compressible Navier-Stokes equations with degenerate viscosity

主讲人：梁之磊

单位：西南财经大学

时间：9月13日9：00

地点：学院一楼报告厅

摘要：The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and three dimensions. It is shown that the density keeps strictly positive from below and above after a finite period of time. Moreover, higher velocity regularity is obtained via a parabolic type iteration technique. Since then the weak solution conserves its energy equality, and decays exponentially to the equilibrium in L2 -norm as time goes to infinity. Moreover, if we assume that the initial momentum is zero, the we prove that the derivatives of the solution have exponential decay rate, and the weak solution becomes a strong one in two dimensional space.

简介：梁之磊， 西南财经大学教授， 博士生导师。从事非线性偏微分方程的研究工作， 主要关心流体力学方程中的数学问题。 在ARMA、JMPA、M3AS、SIAM、Nonlinearity、JDE、Proc. Roy. Soc. Edinburgh等期刊发表多篇学术论文。