Three dimensional stationary solutions of the Electron MHD equations

Abstract

The goal of this paper is to construct non-trivial steady-state weak solutions of the three dimensional Electron Magnetohydrodynamics equations in the class of $H^s\left(T^3\right)$ for some small $s>0$. By exploiting the formulation of the stationary EMHD equations one can treat them as generalized Navier–Stokes equations with half Laplacian. Therefore with convex integration scheme we obtained such stationary weak solutions, which is not yet realizable in the case of classical 3D Navier–Stokes equations.