Estimating the convex relaxation of the ideal magnetohydrodynamics equations

We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the $\mathrm{\Lambda }$-convex hull, the latter providing inequalities which will be satisfied by weak limits of weak solution of the ideal MHD equations, which serve as a model of averaged turbulent magnetohydrodynamical flows.