On global existence, energy decay and blow-up criteria for the Hall-MHD system (Q496734)

In this article the authors study the 3D incompressible Hall-Magnetohydrodynamics system. They show global existence of a unique solution in homogeneous Sobolev or Besov framework for small data together with various time decay properties of the solution. They also give two ``Osgood type'' blow-up criteria for local solutions on a finite interval \((0,T_*)\) when \(t\to T_*\) and they finally prove two Beale-Kato-Majda criteria for local solutions of a related model.