Abstract
This paper intend to study the BMHD system in the whole space $ \mathbb{R}^{2} $ with vertical dissipation, horizontal magnetic dissipation and vertical temperature dissipation.Under the perturbation of hydrostaticequilibrium in a uniform magnetic field, we prove the nonlinear stability by introducing two additional functionals of the horizontalderivative of the velocity and the temperature.Simultaneously, the large-time behavior is also obtained.
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