Global Strong Solutions to the 3D Incompressible Heat-Conducting Magnetohydrodynamic Flows

Abstract

In this article, we prove that there exists a global strong solution to the 3D inhomogeneous incompressible heat-conducting magnetohydrodynamic equations with density-temperature-dependent viscosity and resistivity coefficients in a bounded domain ${\Omega } \subset \mathbb {R}^{3}$ . Let ρ0, u0, b0 be the initial density, velocity and magnetic, respectively. Through some time-weighted a priori estimates, we study the global existence of strong solutions to the initial boundary value problem under the condition that $\|\sqrt {\rho _{0}} u_{0}\|_{L^{2}}^{2} + \|b_{0}\|_{L^{2}}^{2}$ is small. Moreover, we establish some decay estimates for the strong solutions.