Global existence and large time behavior of strong solutions to the Cauchy problem of the 3D heat conducting incompressible MHD flows

Abstract

In this paper, we consider an initial value problem of inhomogeneous heat conducting magnetohydrodynamic equations in R3. Through some time-weighted a priori estimates, we prove the global existence of strong solution provided that (‖ρ0u0‖L22+‖b0‖L22)(‖∇u0‖L22+‖∇b0‖L22) is suitably small, which extends the corresponding Zhong's results [16,17] to the whole space R3. Furthermore, we also derive the algebraic decay estimates of the solution.