Global well-posedness for the Hall-magnetohydrodynamics system in larger critical Besov spaces

Abstract

We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial data in critical Besov spaces that allowing for different integrability indices for the velocity field u and magnetic field b (and its current J), which generalize the result in [13]. Meanwhile, we analyze the long-time behavior of the solutions and get some decay estimates. Finally, a stability theorem for global solutions is established.