In this talk, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\geq 2$. For initial data close to a stable equilibrium in the sense of suitable hybrid Besov norm, we prove that the isentropic compressible Navier-Stokes equations admit global solutions in a certain function space. As a consequence, initial velocity with arbitrary $\dot{B}^{\frac{N}{2}-1}_{2,1}$ norm of the potential part $P^\bot u_0$ 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. (Based workd with Daoyuan FANG and Ruizhao ZI)
Biography
Professor Ting Zhang, School of Mathematical Sciences, Zhejiang University. In 2006, he got his Ph.D. degree from Zhejiang University. His research area is in Nonlinear Partial Differential Equations, and Mathematical Theory in Fluid Mechanics. Much of his research focuses on the study of the local/global well-posedness theory of compressible/inconpressible Navier-Stokes equations and other related systems.