NONUNIQUE WEAK SOLUTIONS IN LERAY--HOPF CLASS FOR THE THREE-DIMENSIONAL HALL-MHD SYSTEM.

Nonunique weak solutions in Leray--Hopf class are constructed for the threedimensional magneto-hydrodynamics with Hall effect. We adapt the widely appreciated convex integration framework developed in a recent work of Buckmaster and Vicol [Ann. of Math., 189 (2019), pp. 101-144] for the Navier--Stokes equation and with deep roots in a sequence of breakthrough papers for the Euler equation. [ABSTRACT FROM AUTHOR]