报告人：李嘉旭（香港中文大学）

时  间：2023年3月7日上午10:00-11:30

地  点：腾讯会议ID：262988310（无密码）

内容摘要:

The barotropic compressible Navier-Stokes system subject to the Navierslip 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.

个人简介：

李嘉旭，香港中文大学数学科学研究所研究助理，博士毕业于中国科学院数学与系统科学研究院。主要从事可压缩Navier-Stokes方程适定性方面的研究, 相关结果发表在ARMA等著名学术期刊上。

联系人：詹伟城