Liouville type Theorems for the stationary compressible 3D MHD equations

TL;DR

This paper establishes Liouville type theorems for smooth solutions of the stationary compressible 3D MHD equations under certain conditions, extending previous results in the field.

Contribution

It generalizes and improves existing Liouville theorems for stationary compressible MHD equations, providing broader conditions for solution triviality.

Findings

Liouville type theorems proved for stationary compressible 3D MHD equations

Conditions under which solutions must be trivial are identified

Results extend previous theorems in the literature

Abstract

In this paper, we investigate the three dimensional stationary compressible Navier-Stokes equations, and obtain Liouville type theorems if a smooth solution $(\rho, \mathbf{u})$ satisfies some suitable conditions. In particular, our results improve and generalize the corresponding result.