【学术报告】 Global existence and decay of solutions to Prandtl system with small analytic data

• 主讲人：Prof. Zhang,Ping, Mathematics Institute of Academy of Mathematics and Systems Science of Chinese Academy of Sciences，Beijing
• 时间：周四20:00-21:00，2020-10-22
• 地点：online

Beijing-Saint Petersburg Mathematics Colloquium (online)

摘要（Abstract） 

In this talk, we shall prove the global existence and the large time decay estimate  of solutions to  Prandtl system with small initial data, which is analytical  in the tangential variable. The key ingredient used in the proof  is to derive sufficiently fast decay-in-time estimate of some weighted analytic energy estimate to a quantity, which consists of a linear combination of the tangential velocity  with its primitive one, and which basically controls the evolution of the analytical radius to the solutions. Our result can be viewed  as a global-in-time Cauchy-Kowalevsakya result for  Prandtl system with small analytical data,which in particular improves the previous result in \cite{IV16} concerning the almost global well-posedness of two-dimensional Prandtl system. In the last part, I shall also mention our recent result on the global well-posedness of this system with optimal Gevrey data. (This is partially joint work with Marius Paicu, Chao Wang and Yuxi Wang).

主讲人简介（Bio）

Director of Mathematics Institute of Academy of Mathematics and Systems Science of Chinese Academy of Sciences; B. S. ，Department of Mathematics of Nanjing University, China, 1991；Ph. D. ，Nanjing University, China, 1997.  Research interests: Navier-Stokes equations and semi-classical analysis.