On the global small solution of 2-D Prandtl system with initial data in the optimal Gevrey class

Abstract

Motivated by [8], we prove the global existence and large time behavior of small solutions to 2-D Prandtl system for data with Gevrey 2 regularity in the x variable and Sobolev regularity in the y variable. In particular, we extend the global well-posedness result in [26] for 2-D Prandtl system with analytic data to data with optimal Gevery regularity in the sense of [11].