Abstract
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 \begin{align*}
\|(u_0,h_0-1)\|_{H_{\mu}^{3,0}}+\|(u_0,h_0-1)\|_{H_{\mu}^{1,2}}+\|(u_0,h_0-1)\|_{H_{\mu}^{2,1}}\le
\varepsilon, \end{align*} then the life
span of the solution is at least of order
$\varepsilon^{-\f43}$.
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