Boundary Layer and Vanishing Viscosity Limit in Magneto-Hydrodynamics
报告题目(Title)：Boundary Layer and Vanishing Viscosity Limit in Magneto-Hydrodynamics
报告人(Speaker)：谢峰（上海交通大学）
地点(Place)：后主楼1223
时间(Time)：6月10日上午9:00-10:00
邀请人(Inviter)：徐桂香
报告摘要
In this talk we will recall the classical Prandtl boundary layer double-scale asymptotical expansions in the analysis of structure of fluids with the high Reynolds number in a domain with boundaries. Vanishing viscosity limit can be regarded as a direct application of Prandtl boundary layer asymptotical expansions. The Prandtl boundary layer theory includes the well-posedness of solutions to the Prandtl boundary layer equations and the justification of Prandtl boundary layer asymptotical expansions etc. Motivated by one open problem in the classical book “Mathematical models in Boundary Layer Theory” by O.A. Oleinik and V.N. Samokhin. We consider the boundary layer theory in Magneto Hydrodynamics. The solvability of MHD boundary layer equations and the validity of Prandtl boundary layer ansatz for MHD equations are studied in Sobolev spaces. Compared with the well-posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for MHD boundary layer any more. Moreover, the validity of Prandtl boundary layer ansatz for MHD is also achieved in Sobolev spaces for some physical parameter regime.
主讲人简介
个人简介：谢峰上海交通大学教授，曾获得德国洪堡学者，上海市科技启明星等荣誉。主要研究流体力学边界层中的数学理论及高温辐射流体力学模型的定性分析。近年来与合作者在流场没有单调性条件的情形下证明了磁流体边界层的稳定性，并在有限阶正则性函数空间中证明了普朗特边界层渐近展开理论适用于二维磁流体力学方程组。在CPAM，SIMA，JDE等重要期刊发表论文三十余篇。
