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 $(u_0,b_0)\in {\dot{B}}_{p,5}^{\frac{3}{p}-1}(\mathbb{R})\times ({\dot{B}}_{p,5}^{\frac{3}{p}-1}(\mathbb{R})\cap {\dot{B}}_{p,1}^{\frac{3}{p}}(\mathbb{R}))$ 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.