Time: 1pm GST
(Mecca — 12pm, noon | Paris — 11am | New York — 5am | Tokyo — 6pm | Beijing — 5pm)
Speaker: Ping Zhang, professor and director, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Abstract
In this paper, we 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. Finally I'll present our recent result concerning the global wellposedness with small Gevrey data. This is a partially joint work with N. Liu; M. Paicu; C. Wang and Y. Wang.
Short CV: Ping Zhang is now professor and director of the institute of mathematics,
The Chinese Academy of Sciences. His research interest is mainly on the global solutions
of incompressible viscouse fluid system. So far, he has published more than 110 papers on the
related filed.