Stability of hydrostatic equilibrium in a uniform magnetic field with mixed partial dissipation

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.