The time evolution of electrically conducting compressible flows under the mutual interactions with the magnetic field is described by the system of magnetohydrodynamics (MHD). In this talk, we focus on the existence of global-in-time weak solutions with large initial data. Firstly, for a simplified 2D MHD model of viscous non-resistive flows, we prove the existence of global-in-time weak solutions by invoking the idea from compressible two-fluid model. Secondly, for the general 3D inviscid resistive MHD system, we prove the existence of infinitely many global-in-time weak solutions for any smooth initial data. To do this, we appeal to the method of convex integration developed by De Lellis and Szekelyhidi and adapted to the compressible flows by Chiodaroli, Feireisl and Kreml.

The results are based on the joint works with Eduard Feireisl and Yongzhong Sun.

The results are based on the joint works with Eduard Feireisl and Yongzhong Sun.