Seminar
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| Location: | SLMath: Online/Virtual |
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
Global Existence And Decay Of Solutions To Prandtl System With Small Analytic And Gevrey Data
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
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 similar result with optimal Gevrey regularity data will be presented. This is partially joint work with M. Paicu; Ning Liu; Chao Wang and Yuxi Wang.
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