In this paper, we consider an initial boundary value problem for the nonhomogeneous heat-conducting magnetohydrodynamic fluids when the viscosity $\mu$, magnetic diffusivity $\nu$ and heat conductivity $\kappa$ depend on the temperature $\theta$ according to $\mu(\theta)=\theta^{\alpha}$, $\ \kappa(\theta)=\theta^{\beta}$, $\nu(\theta)=\theta^{\gamma}$, with $\alpha$, $\gamma>0$, $\beta\geq 0$. We prove the global existence of a unique strong solution provided that $\|\sqrt{\rho_0}u_0\|_{L^2}^2+\|H_0\|_{L^2}^2+\beta\|\sqrt{\rho_0}\theta_0\|_{L^2}^2$ is suitably small. In addition, we also get some results of the large-time behavior and exponential decay estimates.
Qingyan LI
,
Zhenhua GUO
. GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS[J]. Acta mathematica scientia, Series B, 2025
, 45(3)
: 951
-981
.
DOI: 10.1007/s10473-025-0312-6
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