**The speaker:** Professor Ping Zhang (Kyoto University).

**Title of the talk:** “Global existence and decay of solutions to Prandtl system with small analytic and Gevrey data”.

**Time:** Thursday, 3 of June 2021, 16:00 - 17:00.

**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.

ZOOM link:

https://us02web.zoom.us/j/83673138944?pwd=azQyc1BwUjJFY3VjMStLbFR5Z2VwUT09

ZOOM Id: 836 7313 8944

Passcode: 808818

We are pleased to inform you that the information on previous talks is available on the seminar web page https://researchseminars.org/seminar/Cafe_Analysis_and_Fluid see Past Talks section.

* Organizing Committee:* Professors Zhen Lei, Mikhail Korobkov, Adele Ferone, Remigio Russo and Konstantin Pileckas.

This seminar is organized by Fudan University (Shanghai, China) with the collaboration of Universita degli studi della Campania "Luigi Vanvitelli" (Caserta, Italy) and Vilnius University (Vilnius, Lithuania). This seminar is meant to gather renowned experts working on Geometric and Real Analysis with applications to PDEs and Mathematical Physics and represents an opportunity for presenting high-impact research, as well as facilitating the exchange of ideas between researchers.

2021-06-01