报告题目：Global Well-posedness of Compressible Navier-Stokes Equations with Large Data

报告时间：2022-07-15  15:30-16:30

报告人：李竞 研究员  南昌大学&中科院数学与系统科学研究院

腾讯会议ID：747-259-555 密码：0715

报告入口：https://meeting.tencent.com/dm/i92k09ITKsw4

Abstract：The barotropic compressible Navier-Stokes system subject to the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain is considered. For initial density allowed to vanish, the global existence of strong and weak solutions is established when the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. It should be mentioned that this result is obtained without any restrictions on the size of initial value. To get over the difficulties brought by boundary, on the one hand, Riemann mapping theorem and the pull-back Green's function method are applied to get a pointwise representation of the effective viscous flux. On the other hand, since the orthogonality is preserved under conformal mapping due to its preservation on the angle, the slip boundary conditions are used to reduce the integral representation to the desired commutator form whose singularities can be cancelled out by using the estimates on the spatial gradient of the velocity. This is a joint work with Xinyu FAN and Jiaxu LI.