On the weak solutions for the MHD systems with controllable total energy and cross helicity

Changxing Miao, Weikui Ye

In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in $C([0,T];L^2({\mathbb{T}}^3))$ for any initial data in $H^{{\bar{\hat{I}}}^2}({\mathbb{T}}^3)$…