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 Ω⊂ℝ3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Omega } \subset \mathbb {R}^{3}$\end{document}. 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 ∥ρ0u0∥L22+∥b0∥L22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\|\sqrt {\rho _{0}} u_{0}\|_{L^{2}}^{2} + \|b_{0}\|_{L^{2}}^{2}$\end{document} is small. Moreover, we establish some decay estimates for the strong solutions.