Almost sure existence of global weak solutions for supercritical electron MHD

Abstract

We consider the Cauchy problem for the electron magnetohydrodynamics model in the supercritical regime. For rough initial data in ${\mathcal{H}}^{-s}({\mathbb{T}}^n)$ with $s>0$, we obtain global in time weak solutions almost surely via an appropriate randomization of the initial data.

28 pages