Title: Global Strong Solution of a 2D coupled Parabolic-Hyperbolic Magnetohydrodynamic System,
Abstract: The main objective of this paper is to study the global strong solution of
the parabolic-hyperbolic incompressible magnetohydrodynamic (MHD) model in two
dimensional space. Based on Agmon, Douglis and Nirenberg's estimates for the
stationary Stokes equation and the Solonnikov's theorem of
$L^p$-$L^q$-estimates for the evolution Stokes equation, it is shown that the
mixed-type MHD equations exist a global strong solution.