Conditional Liouville theorems for the Navier-Stokes equations

TL;DR

This paper introduces a new approach to the Liouville problem for stationary Navier-Stokes equations, providing improved conditional theorems based on assumptions about the velocity's antiderivative.

Contribution

It develops a novel method for the Liouville problem, yielding stronger conditional theorems for stationary Navier-Stokes equations.

Findings

Proves new conditional Liouville theorems

Improves upon previous results with less restrictive assumptions

Enhances understanding of stationary Navier-Stokes solutions

Abstract

We present a novel approach to the Liouville problem for the stationary Navier-Stokes equations. As an application of our method, we prove conditional Liouville theorems with assumptions on the antiderivative of the velocity that represent substantial improvements on what was heretofore known.