On some Liouville type Theorems for the stationary MHD and Hall-MHD equations

TL;DR

This paper establishes Liouville type theorems for stationary MHD and Hall-MHD equations, demonstrating under certain conditions that the velocity and magnetic fields must be trivial.

Contribution

It proves new Liouville theorems for stationary MHD and Hall-MHD equations under Lorentz space and decay assumptions.

Findings

Velocity and magnetic fields are zero under specified conditions.

Results apply to fields in Lorentz spaces or with decay assumptions.

Extends Liouville theorems to MHD and Hall-MHD contexts.

Abstract

We prove several Liouville type results for the stationary MHD and Hall-MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces or satisfying a priori decay assumption, must be zero.