Ergodicity of stochastic Magneto-Hydrodynamic equations driven by α-stable noise

The current paper is devoted to the ergodicity of stochastic Magneto-Hydrodynamic equations driven by α  -stable noise with α∈(32,2). By the maximal inequality for the stochastic α-stable convolution and vorticity transformation, the well-posedness of the mild solution for stochastic Magneto-Hydrodynamic equation is established. Due to the discontinuous trajectories, the existence and uniqueness of the invariant measure for stochastic Magneto-Hydrodynamic equation are obtained by the strong Feller property and the accessibility to zero instead of the irreducibility.