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

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}.

References in corpus (3)

• Boundary layer separation and local behavior for the Steady Prandtl equation
• Global existence and decay of solutions to Prandtl system with small analytic data
• Global small analytic solutions of MHD boundary layer equations