Global small solutions of MHD boundary layer equations in Gevrey function space

TL;DR

This paper proves the existence of global small solutions and decay estimates for the MHD boundary layer equations in Gevrey space, extending previous analytic space results without structural assumptions.

Contribution

It establishes global well-posedness of MHD boundary layer equations in Gevrey b3/2 space using new auxiliary functions and refined analysis, without structural assumptions.

Findings

Global small solutions are obtained in Gevrey space.

Decay estimates for solutions are established.

The method overcomes derivative loss issues in boundary layer analysis.

Abstract

In this paper, we obtain global small solutions and decay estimates for the MHD boundary layer in Gevrey space without any structural assumptions, generalizing the results of \cite{NL} in analytic space. The proof method is mainly inspired by \cite{WXLY} and \cite{CW}, using new auxiliary functions and finer structural analysis to overcome the difficulty of the loss of derivatives and then we obtain the global well-posedness of the MHD boundary layer in the Gevrey $\frac{3}{2}$ space.