In this talk I will survey some recent progress on the analysis of the Prandtl’s boundary layer equations. In particular, a construction of Holder continuous secondary flow for 3-dimensional viscous boundary flows. Such a flow can be constructed by the methods of convex integration. Some ideas and techniques along this line will be presented.
A Brief Biography:
Professor Zhouping Xin is an expert in the areas of partial differential equations, mathematical physics, fluid mechanics, nonlinear waves, numerical analysis and numerical methods for PDEs and applied mathematics. He has made some substantial contributions to the stability theory linear and nonlinear waves, boundary layer theory, multi-dimensional shock wave theory, vortex methods and relaxation methods, transonic flows, and Navier-Stokes systems with more than one hundred publications in leading international research journals. After got his Ph. D in mathematics from the University of Michigan (Ann Arbor) in 1988, Professor Xin became a Courant instructor at The Courant Institute of New York University, where he was promoted to be a full professor of mathematics in 1995. In 2000, Professor Xin moved from the New York University to the Chinese University of Hong Kong where he has been the William M. W. Mong Professor of Mathematics and the associated director of the Institute of Mathematical Sciences until now. Professor Xin got many honors including: Sloan Research Fellow (1991-1993, USA), Presidential Fellow (1993, NYU, USA); ICM invited speaker (2002); and Morningside Gold Medalist in Mathematics (2004).
Professor Xin is the co-editor-in-chief of MAA, associated editor of M2as, and member of the editorial boards for many journals such as SIMA, M3AS, Kyoto J. Math., and Sciences China Mathematics, etc..