Stability for the Magnetic Bénard System with Partial Dissipation

In this paper, we prove the global existence and stability of the magnetic Bénard system with partial dissipation on perturbations near a background magnetic field in \({\mathbb {T}}^d (d=2,3)\) ${\mathbb{T}}^d(d=2,3)$ . If there is no velocity dissipation, the stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit large-time decay rate of the solutions.