Well-posedness for the Incompressible Hall-MHD Equations in Low Regularity Spaces

Abstract

In this paper, we first establish the local well-posedness of strong solutions to the Cauchy problem of the incompressible viscous resistive Hall-MHD equations in $$H^s(\mathbb {R}^3)$$ $$(\frac{3}{2}< s\le \frac{5}{2})$$ , and then we prove that the local solution is global when the initial data is small enough.