Global Existence And Asymptotic Behavior Of Classical Solutions To The Compressible Magnetohydrodynamic Equations With Coulomb Force

Nonlinear hyperbolic-parabolic coupled equations has important applications in many fields such as aviation,meteorology,air dynamics and so on,they have rich physical significance and application value.So nonlinear hyperbolic-parabolic coupled equations are hot issues in the modern partial differential equations.The compressible magnetohydrodynamic equations with Coulomb force is a class of typical nonlinear hyperbolic parabolic coupled equations.The existence,uniqueness and asymptotic behavior of solutions are core problems of partial differential equations.The existence,uniqueness and asymptotic behavior of solutions to the initial value problem for the compressible magnetohydrodynamic equations with Coulomb force are still open problems,so the study of these problems has important theoretical significance and practical value.In this paper,we consider the initial value problem for the compressible magnetohydrodynamic equations with Coulomb force in three and higher space dimensions.Global existence and decay estimate of classical solutions are established.The proof is mainly based on the decay properties of solution operator to compressible magnetohydrodynamic equations with Coulomb force,which may be derived from the pointwise estimate of the solution operator to a linear wave equation,while the pointwise estimate of solution operator to the linear wave equation may be established by the energy method in the Fourier space.