# 澳门金沙网址

Global well-posdness of Prandtl system with small analytic data

In this paper, we prove the global well-posedness of 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 of the tangent velocity, which is based on a Poincar\'e type inequality and a subtle interplay between the tangential velocity equation and its primitive one.

Our result can be viewed as a global-in-time Cauchy-Kowalevsakya result for Prandtl system with small analytical data.