Seminar in Analysis and Geometry

The talk will be devoted to explain how to construct weak solutions to 3D Ideal MHD equations obtained by convex integration (in the non smooth regime). We will show the existence of bounded weak solutions dissipating energy and cross helicity but preserving magnetic helicity and of critical solutions, in the L^p regime, dissipating magnetic helicity. It turns out that is useful to decouple the system in the magnetic and fluid part, and treat the magnetic part using the Maxwell 2 form. The dissipation of magnetic helicity builds on an anisotropic staircase laminate for the Maxwell systems which might be of independent interest. This is a joint work with Sauli Lindberg (University of Helsinki) and László Székelyhidi (University of Leipzig).