报告人: 訾瑞昭（华中师范大学sunbet中国官网）

报告题目: Global solutions to the isentropic compressible Navier-Stokes equations with a class of large initial data

报告人简介: 訾瑞昭博士，2013年博士毕业于浙江大学，现为华中师范大学sunbet中国官网讲师，主要研究方向为流体力学中的偏微分方程（可压缩与不可压缩流体）：Navier-Stokes 方程，liquid crystal flows，Oldroyd-B model。在Archive for Rational Mechanics and Analysis、Journal of Functioal Analysis、Journal of Differential Equations等国际主流数学杂志发表论文10余篇。    

报告摘要：In this talk, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\ge2$. In order to better reflect the dispersion nature of this system, we introduce a new solution space that characterizes the behaviors of the solutions  in different frequencies,  and prove that the isentropic compressible Navier-Stokes equations admit global solutions when the initial data are close to a stable equilibrium in the sense of suitable hybrid Besov norm.   As a consequence, the initial velocity with arbitrary $\dot{B}^{\fr{N}{2}-1}_{2,1}$ norm of potential part $\Pe^\bot u_0$  and large highly oscillating  are allowed in our results. The proof relies heavily on the dispersive estimates for  the system of acoustics, and a careful study of the nonlinear terms.

报告时间：2017年3月21日10:00-11:00

报告地点:科技楼南楼702