On the global existence to Hall-MHD system

Abstract

<p style='text-indent:20px;'>This paper investigates the well-posedness of Hall-magnetohydrodynamics system. By using a new current function <inline-formula><tex-math id="M1">\begin{document}$ J = \nabla\times B $\end{document}</tex-math></inline-formula> as an additional unknown. The mild solution of Hall-MHD exists globally in the nonhomogeneous Lei-Lin space setting provided that the initial data satisfies <inline-formula><tex-math id="M2">\begin{document}$ \|u_{0}\|_{\mathcal{X}^{-1} }+\|B_{0}\|_{ \mathcal{X}^{-1}}+\|J_{0}\|_{ \mathcal{X}^{-1}}&lt;\min \{\frac{\mu }{2}, \frac{\nu }{2}\}. $\end{document}</tex-math></inline-formula></p>