Logarithmic improvement of a Liouville-type theorem for the stationary Navier--Stokes equations

TL;DR

This paper proves a new Liouville-type theorem for stationary Navier-Stokes equations in three dimensions, improving previous results by incorporating a logarithmic factor related to the velocity field's growth at infinity.

Contribution

It introduces an enhanced Liouville theorem that accounts for logarithmic growth, advancing understanding of solutions' behavior at infinity in the stationary Navier-Stokes context.

Findings

Established a logarithmic improvement of the Liouville theorem

Characterized the $L^p$ growth of velocity fields at infinity

Extended the class of solutions for which triviality holds

Abstract

We establish a new Liouville-type theorem for the stationary Navier--Stokes equations in $\mathbb{R}^3$. The main result is an improvement of the previous result with a logarithmic factor based on an understanding of $L^p$ growth of the velocity field near infinity.