# On well-posedness of generalized Hall-magneto-hydrodynamics

## TL;DR

This paper establishes local well-posedness for the generalized Hall-magneto-hydrodynamics system in specific Besov spaces and demonstrates global well-posedness for the generalized electron magneto-hydrodynamics system with small initial data.

## Contribution

It provides new well-posedness results for generalized Hall-magneto-hydrodynamics systems in Besov spaces, including global results for the electron magneto-hydrodynamics case.

## Key findings

- Local well-posedness in Besov spaces for generalized Hall-magneto-hydrodynamics.
- Global well-posedness for generalized electron magneto-hydrodynamics with small initial data.
- Identification of suitable Besov space conditions for well-posedness.

## Abstract

We obtain local well-posedness result for the generalized Hall-magneto-hydrodynamics system in Besov spaces ${\dot B^{-(2\alpha_1-\gamma)}_{\infty, \infty}} \times {\dot B^{-(2\alpha_2-\beta)}_{\infty,\infty}(\mathbb R^3)}$ with suitable indexes $\alpha_1, \alpha_2, \beta$ and $\gamma.$ As a corollary, the generalized electron magneto-hydrodynamics system is globally well-posed in ${\dot B^{-(2\alpha_2-2)}}_{\infty, \infty}(\mathbb R^3)$ for small initial data.