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

TL;DR

This paper proves the global existence and long-term behavior of small solutions to the 2-D Prandtl system with initial data in the optimal Gevrey class, extending previous results to less regular data.

Contribution

It extends the global well-posedness of the 2-D Prandtl system from analytic to optimal Gevrey regularity in the initial data.

Findings

Global existence of small solutions established

Large time behavior characterized

Extension from analytic to optimal Gevrey regularity

Abstract

Motivated by \cite{DG19}, 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 \cite{PZ5} for 2-D Prandtl system with analytic data to data with optimal Gevery regularity in the sense of \cite{Ger1}.