Liouville type theorems for the stationary Hall-MHD equations in local Morrey spaces

TL;DR

This paper proves that under certain conditions in local Morrey spaces, solutions to the 3D stationary Hall-MHD equations must be trivial, extending classical results for Navier-Stokes equations.

Contribution

It establishes Liouville type theorems for stationary Hall-MHD equations in local Morrey spaces, generalizing previous results for Navier-Stokes.

Findings

Solutions are identically zero under specified conditions

Extends Liouville theorems to Hall-MHD equations

Includes results for classical MHD equations

Abstract

This paper is concerned with the Liouville type theorems for the 3D stationary incompressible Hall-MHD equations. We establish that under some sufficient conditions in local Morrey spaces, solutions of the stationary Hall-MHD equations are identically zero. In particular, we also prove Liouville type results for the stationary incompressible MHD equations on $\mathbb{R}^3$. Our theorems extend and generalize the classical results for the stationary incompressible Navier-Stokes equations.