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Non-unique weak solutions in Leray-Hopf class are constructed for the threedimensional magneto-hydrodynamics with Hall effect. We adapt the widelyappreciated convex integration framework developed in a recent work ofBuckmaster and Vicol for the Navier-Stokes equation, and with deep roots in asequence of breakthrough papers for the Euler equation.

Non-unique weak solutions in Leray-Hopf class of the 3D Hall-MHD system