Asymptotic stability and decay rates for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity

摘要

We consider the asymptotic stability and large-time behavior for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity. More precisely, we acquire the asymptotic stability and decay rate for the system on two perturbations near two steady state solutions (u˜,b˜,θ˜,p˜) and (uˇ,bˇ,θˇ,pˇ), respectively.