偏微分方程研讨班：Inviscid limit of Navier Stokes equations with vortex sheet initial data

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Chao Wang ( Peking University)

题  目：Inviscid limit of Navier Stokes equations with vortex sheet initial data

时  间：2023.04.10（星期一）10:30-11:30

地  点：数学院南楼N913

摘  要：In this talk, I will talk about the inviscid limit of 2-D incompressible Navier-Stokes equations in the whole space with vortex sheet initial data. Although the initial data have different velocities along the tangential direction of one interface, we still can prove that the Navier-Stokes equations admit a smooth solution whose regularity depends on the viscosity. When the viscosity equals to zero, the system becomes the Euler equations whose velocities have a jump across a boundary. Due to the mismatch of the velocity on the interface, same phenomenon as boundary layer will appear. Like the boundary layer theory, to justify the inviscid limit, there appears one derivative loss. In this paper, we improve the energy method to justify the inviscid limit in the analytic setting. This work is joint with Prof. Yuxi Wang and Prof. Zhifei Zhang.