Well-posedness for the Hall-magnetohydrodynamics system in critical space

Abstract

In this paper, we investigate the well-posedness of the Cauchy problem to 3D incompressible Hall-magnetohydrodynamic system in critical Besov paces. Inspired by Paicu and Zhang's work in [26], we consider the initial data‖(u0h,b0h,J0)‖B˙p,13p−1exp⁡{C0(1+12μ+12ν)K1}≤c, with K1=C0‖(u03,b03)‖B˙p,13p−1+[(1μ+1ν)+(1+1ν)2] and a small constant c>0, which also admit a global solution. Our Theorem improves the result in [13].