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 alpha-stable noise with alpha is an element of (3/2, 2). By the maximal inequality for the stochastic alpha-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. (C) 2016 Elsevier Inc. All rights reserved.