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

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 < subset of>3. Let (0), u(0), b(0) 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 vertical bar b0 vertical bar L22 is small. Moreover, we establish some decay estimates for the strong solutions.