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${\Omega } \subset \mathbb {R}^{3}$. 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 ∥ρ0u0∥L22+∥b0∥L22$\|\sqrt {\rho _{0}} u_{0}\|_{L^{2}}^{2} + \|b_{0}\|_{L^{2}}^{2}$ is small. Moreover, we establish some decay estimates for the strong solutions.

中文翻译：

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3D 不可压缩导热磁流体动力流动的全球强解

在本文中，我们证明了在有界域Ω⊂ℝ3${\Omega } \subset \mathbb { 具有密度-温度依赖的粘度和电阻率系数的3D非均匀不可压缩导热磁流体动力学方程存在全局强解R}^{3}$。设 ρ0、u0、b0 分别为初始密度、速度和磁力。通过一些时间加权的先验估计，我们研究了在 ∥ρ0u0∥L22+∥b0∥L22$\|\sqrt {\rho _{0}} u_{ 条件下初边值问题强解的全局存在性0}\|_{L^{2}}^{2} + \|b_{0}\|_{L^{2}}^{2}$ 很小。此外，我们为强解建立了一些衰减估计。