北航数学论坛学术报告

                                             —— Global existence and decay of solutions to Prandtl system with small analytic data

张平

（中科院数学院研究员）

报告题目: Global existence and decay of solutions to Prandtl system with small analytic data

报告人： 张平（中科院数学院研究员）

报告时间：11月4日15：30—16：30

报告地点：沙河校区主楼E-404

报告摘要: 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 Ning Liu， Marius Paicu, Chao Wang and Yuxi Wang)

报告人简介：张平，现任中科院数学与系统科学研究院研究员，数学研究所所长。曾获国家杰出青年基金；第十届中国青年科技奖; 国家自然科学二等奖；教育部长江特聘教授(中国科学院大学)； 中国数学会陈省身奖等奖项。自1997年以来，共在Comm. Pure Appl. Math.，Ann. Sci. École Norm. Sup. , Arch. Ration. Mech. Anal.， Comm. Math. Phys.，Adv. Math.， J. Reine Angew. Math.等杂志发表文章100余篇，在美国数学会出版专著一本。

邀请人：韩德仁