On well-posedness of generalized Hall-magneto-hydrodynamics

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