The Well-Posedness of Three-Dimensional Hall-Magnetohydrodynamics Model with Partial Viscosity Terms

The paper is concerned with three-dimensional Hall-magnetohydrodynamics for partial viscosity terms. By applying basic inequality and energy estimates, we prove the global existence of classical solution for small initial data. Additionally, the local existence of classical solution is also obtained. The smallness conditions are given by the suitable Sobolev norms. Furthermore, the existence of classical solutions with large initial data can be obtained when the coefficients of viscosity sufficiently large.