Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space

Abstract

In this paper, we study the long time well-posedness of 2-D MHD boundary layer equation. It was proved that if the initial data satisfies

$$\|(u_0,h_0-1)\|_{H_{\mu}^{3,0}\cap H_{\mu}^{1,2}}\le \varepsilon,$$ then the life span of the solution is at least of order $\varepsilon^{2-\eta}$ for $\eta>0$.