On some Liouville type theorems for the stationary equations of MHD

TL;DR

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

Contribution

It provides new Liouville theorems for stationary MHD equations with fields in Lorentz spaces, extending previous results to more general function spaces.

Findings

Velocity and magnetic fields in specified Lorentz spaces must be zero.

Theorems apply to stationary Hall-MHD and MHD equations.

Results generalize classical Liouville theorems to Lorentz space settings.

Abstract

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