Existence of Global Strong Solutions for Vlasov-Fokker-Planck-MHD Equations

In this paper, we consider the global well-posedness of the solution of the initial-boundary value problem of the one-dimensional Vlasov-MHD system. The equations are composed of magnetohydrodynamics equations with viscosity (MHD) and Vlasov-Fokker-Planck equations, which describe the motion of uncharged particles in a viscous, heterogeneous, compressible conductive fluid. In this paper, we prove the existence of global strong solutions of the equations by using the method of energy estimation and the reflection boundary conditions of particle motion.