Large time behavior for the Hall-MHD equations with horizontal dissipation

Abstract

This paper examines the large time behavior of solutions to the 3D Hall-magnetohydrodynamic equations with horizontal dissipation. As preparations we establish the global well-posedness of solutions and their global explicitly uniform upper bounds for Hk (k ≥ 1) to this system with initial data small in H2. Furthermore, if the initial data also belongs to homogeneous negative Besov spaces, we prove the optimal decay rates of the aforementioned global solutions and their higher order derivatives.