Notes on Liouville type Theorems for the stationary compressible Navier-Stokes equations

TL;DR

This paper establishes Liouville type theorems for three-dimensional stationary compressible Navier-Stokes equations, broadening previous results by Li and Yu, under specific smoothness and condition assumptions.

Contribution

It improves and generalizes existing Liouville theorems for stationary compressible Navier-Stokes equations with new conditions.

Findings

Liouville type theorems proved under new conditions

Generalization of previous results by Li and Yu

Enhanced understanding of stationary solutions

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 of Li and Yu (2014) [8].