Well-posedness of the relaxed Electron MHD equations with random diffusion

Abstract

We investigate a three-dimensional active-vector relaxation of the electron magnetohydrodynamics (EMHD) equations without resistivity. The relaxation replaces the electron current by a generalized current defined through a fractional power of the Laplacian. We drive the system by multiplicative pseudo-differential noise and apply an exponential transformation that removes the stochastic differential term and produces an effective fractional damping. For deterministic divergence-free, mean-zero initial data, we prove local well-posedness up to a stopping time in suitable Gevrey spaces. Under a smallness condition, we further establish global well-posedness with high explicit probability.

arXiv comment18 pages