Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Feng Xie，Shanghai Jiao Tong University
Inviter:	李竞研究员
Title:	Stability of Boundary Layer and Vanishing Viscosity Limit in Magneto-Hydrodynamics
Time & Venue:	2019.6.11 15:00 N212
Abstract:	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.