张伟博士后，首都师范大学

In this talk, time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We will discuss how to get global well-posedness of the problem for small initial data in scale invariant critical Besov spaces by maximal $L^1$-regularity of the corresponding Stokes problem in the half-space. In this talk，we will introduce maximal $L^1$-regularity for the Stokes flow in the half-space for 0-boundary data, then we can construct the solution formula of the Stokes equation and the Littlewood-Paley decomposition with separation of variables.