On well-posedness of generalized Hall-magneto-hydrodynamics

Abstract

We obtain local well-posedness result for the generalized Hall-magneto-hydrodynamics system in Besov spaces ${\dot{B}}_{\infty ,\infty }^{-(2\hat{I}{\pm }_1-{\hat{I}}^3)}\times {\dot{B}}_{\infty ,\infty }^{-(2\hat{I}{\pm }_2-{\hat{I}}^2)}({\mathbb{R}}^3)$ with suitable indexes $\hat{I}{\pm }_1,\hat{I}{\pm }_2,{\hat{I}}^2$ and ${\hat{I}}^3.$ As a corollary, the generalized electron magneto-hydrodynamics system is globally well-posed in ${{\dot{B}}^{-(2\hat{I}{\pm }_2-2)}}_{\infty ,\infty }({\mathbb{R}}^3)$ for small initial data.