# Remarks on Liouville Type Theorems for Steady-State Navier-Stokes Equations

## TL;DR

This paper proves Liouville type theorems for steady-state Navier-Stokes equations under specific assumptions inspired by heat equation conditions with divergence-free drift, advancing understanding of solutions' behavior.

## Contribution

It introduces new Liouville theorems for stationary Navier-Stokes equations based on assumptions motivated by heat equation conditions with divergence-free drift.

## Key findings

- Liouville theorems established under certain assumptions.
- Conditions inspired by heat equations with divergence-free drift.
- Enhanced understanding of steady-state Navier-Stokes solutions.

## Abstract

Liouville type theorems for the stationary Navier-Stokes equations are proven under certain assumptions. These assumptions are motivated by conditions that appear in Liouvile type theorems for the heat equations with a given divergence free drift.