关键词: MHD 方程, 薄区域, 渐进分析

Abstract: Based on the global existence of strong solution of MHD equations on three dimensional thin domain, asymptotic expansion for the strong solution (u,h) of
MHD equations is obtained, and this expansion holds uniformly for
all the time t≥0. When ε, the thickness of the
domain, is small, the strong solution (u,h) of MHD equations can
be formally expressed as
u=\bar{u}(t)+u_p+U,\quad
h=\bar{h}(t)+h_p+H,\quad \forall t≥0,

or
u=\bar{u}(t)+u_s+U^{\star},\quad
h=\bar{h}(t)+h_s+H^{\star},\quad \forall t≥0,
where (\bar{u},\bar{h}) is a solution of 2D-3C MHD equations, (u_{p},h_p) is a solution of P-S MHD equations, u_s,h_s are respectively solutions of two Stokes equations, (U,H),(U^\star,H^\star)
are two function pairs depending only on the initial data. (U,H) and (U^\star,H^\star)
are small with respect to
\varepsilon. (u_{p},h_p) and u_{s},h_s are smaller. And the convergence of the expansion is proved.

Key words: MHD equations, Thin domains, Asymptotic analysis