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We show that ideal 2D MHD does not possess weak solutions (or evensubsolutions) with compact support in time and non-trivial magnetic field. Wealso show that the $\Lambda$-convex hull of ideal MHD has empty interior inboth 2D and 3D; this is seen by finding suitable $\Lambda$-convex functions. Asa consequence we show that mean-square magnetic potential is conserved in 2D bysubsolutions and weak limits of solutions in the physically natural energyspace $L^\infty_t L^2_x$, and in 3D we show the conservation of magnetichelicity by $L^3$-integrable subsolutions and weak limits of solutions.However, in 3D the $\Lambda$-convex hull is shown to be large enough thatnontrivial smooth, compactly supported strict subsolutions exist.

Magnetic helicity and subsolutions in ideal MHD