Three dimensional stationary solutions of the Electron MHD equations

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 $H^s({\mathbb{T}}^3)$ 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.