Estimating the convex relaxation of the ideal magnetohydrodynamics equations

Abstract

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 $\Lambda$-convex hull, the latter providing inequalities which will be satisfied by weak limits of weak solutions of the ideal MHD equations, which serve as a model of averaged turbulent magnetohydrodynamical flows.