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 ‖(u0, h0 − 1)‖H3,0 μ ∩H1,2 μ ≤ ε, then the life span of the solution is at least of order ε2−η for η > 0.