偏微分方程研讨班：MHD Boundary Layers Well-Posedness Theory Theory in Sobolev Spaces

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：廖家江（北京应用物理与计算数学研究所）   

题  目：MHD Boundary Layers Well-Posedness Theory Theory in Sobolev Spaces (I)

时  间：2022.09.03（星期六）下午15:00-16:00

地  点：腾讯会议：650-702-296

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题  目：MHD Boundary Layers Well-Posedness Theory Theory in Sobolev Spaces(II)

时  间：2022.09.03（星期六）下午16:00-17:00

地  点：腾讯会议：650-702-296

摘 要：We study the well-posedness  theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl-type equations that are derived from the incompressible MHD system with non-slip boundary condition on the velocity and perfectly conducting condition on the magnetic field. Under the assumption that the initial tangential magnetic field is not zero, we establish the local-intime existence, uniqueness of solutions for the nonlinear MHD boundary layer equations. In this talk, we will establish a priori estimates for the equation of boundary layers. Firstly, we consider the weighted H_l^m-estimates with normal derivatives.