Global existence of solutions for the Hall-MHD equations

Abstract

In this paper, we study the global well-posedness of the incompressible Hall-MHD system for small initial data $( u_0, b_0) \in \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \times \Big( \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \cap \dot B^{\frac3p}_{p,1}(\mathbb{R}) \Big)$ for $1 < p < 5$. We get the result under the weaker regularity and integrability conditions of the initial data than the previous works. We also give integral formulae for the solution.