Local Existence Of Solutions To The Magnetohydrodynamic Equation In R₊ⁿ⁺¹

The local existence and uniqueness of the solution to the magnetohydrodynamics equa-tions(for brevity, we call it MHD equation) in R+n+1={(x, xn+1)∈Rn+1;x∈Rn, xn+1> 0} are considered in this paper. To this end, we first prove some properties of the Stokes operator and prove that it generate an analytic semi-group on the Besov spaces with negative order, then give the local existence and uniqueness of the solution to the MHD equation by using the fixed point theorem.