Long time well‐posedness of two dimensional Magnetohydrodynamic boundary layer equation without resistivity

摘要

This paper investigates the long time well‐posedness of 2‐D MHD boundary layer equation without resistivity. It is proved that if the initial data satisfies ‖(u0,h0−1)‖Hμ3,0+‖(u0,h0−1)‖Hμ1,2+‖(u0,h0−1)‖Hμ2,1≤ε,$$ {leftVert left({u}_0,{h}_0-1right)rightVert}_{H_{mu}#x0005E;{3,0}}#x0002B;{leftVert Big({u}_0,{h}_0-1Big)rightVert}_{H_{mu}#x0005E;{1,2}}#x0002B;{leftVert Big({u}_0,{h}_0-1Big)rightVert}_{H_{mu}#x0005E;{2,1}}le varepsilon, $$ then the life span of the solution is at least of order ε−43$$ {varepsilon}#x0005E;{-frac{4}{3}} $$.