勷勤数学•领军学者报告

题      目：Some Recent Results on Compressible Navier-Stokes Equations

报  告  人：李竞 教授  (邀请人：袁源)

                                     中科院数学与系统科学研究院

时      间： 11月13日  10：30-11：30

地     点：数科院西楼111报告厅

报告人简介:

        李竞，研究员，中科院数学与系统科学研究院，2015年获得国家杰出青年基金资助。主要研究方向为可压缩Navier-Stokes方程，李竞研究员证明了三维空间可压缩Navier-Stokes方程含真空的大震荡古典解的整体存在性等一系列重要结果，其研究工作发表在国际著名数学杂志“Comm. Pure Appl. Math.”、“Arch. Ration. Mech. Anal.”、“Ann PDE”“ Comm. Math. Phys.”、“J. Math. Pures Appl. ” 和“ SIAM J. Math. Anal.”。

摘      要：

       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.

        欢迎老师、同学们参加、交流！