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.

13 pages

References in corpus (1)

• Global Strong solution with vacuum to the 2D nonhomogeneous incompressible MHD system