Global existence of strong solutions to the 3D incompressible magnetohydrodynamics equations with zero heat-conduction

Abstract

In this paper, we study an initial-boundary value problem of three-dimensional inhomogeneous incompressible magnetohydrodynamics (MHD) fluids with vacuum, zero heat-conduction and density-temperature-dependent viscosity and magnetic diffusive coefficients. Based on the time-weighted a priori estimates, we establish the global existence and exponential decay properties of strong solutions under the conditions that the initial energy is suitably small.