Well-posedness for the incompressible Hall-MHD system with initial magnetic field belonging to $H^{\frac{3}{2}}(\mathbb{R}^3)$

Abstract

In this paper, we first prove the local well-posedness of strong solutions to the incompressible Hall-MHD system with initial data (uIn particular, if the viscosity coefficient is equal to the resistivity coefficient, we can reduce σ to 0 with the aid of the new formulation of the Hall-MHD system observed by [11]. Moreover, we establish the global well-posedness in H 1 2 +σ (R 3 ) × H 3 2 (R 3 ) with σ ∈ (0, 2) for small initial data and get the optimal time-decay rates of solutions. Our results improves some previous works.