Invited by Prof.Yuexun Wang of School of Mathematics and Statistics, Prof. Jinkai Li from South China Research Center for Applied Mathematics and Interdisciplinary Studies，South China Normal Universitywill give a lecture.

Title: Commutator estimates on bounded domains and applications to IBVP to compressible Navier-Stokes equations

Time: 10:00 a.m.,Jul. 13th, 2021

Location: Room 518, Polytechnic building

Abstract: In this talk, we will present estimates on two kinds of commutators defined on bounded domains: one is a natural extension in the case of general bounded domains of the classic Riesz commutator and the other is that of the spatial derivatives with the solution mapping of the co-normal derivative problem of the Laplacian. These two kinds of commutators arise in studying the IBVP to the compressible Navier-Stokes equations with Navier slip boundary conditions. As an application of these commutator estimates as well as a BMO estimate for the gradient of solutions to the Lame system subject to the Navier slip boundary conditions, we establish the global well-posedness of strong solutions to the isentropic compressible Navier-Stokes equations with general Navier slip boundary conditions on general boundary domains, under the condition that the initial energy is small. The initial vacuum is allowed.