Liouville Type Theorem for Stationary Navier-Stokes Equations

TL;DR

This paper proves that smooth solutions to the stationary Navier-Stokes equations in three-dimensional space, which are globally in L6 and BM0^{-1} spaces, must be trivial (zero).

Contribution

It establishes a Liouville type theorem for stationary Navier-Stokes equations under specific integrability and regularity conditions.

Findings

Any smooth solution with the given conditions is zero.

The result extends Liouville theorems to broader function spaces.

Provides conditions ensuring triviality of solutions.

Abstract

It is shown that any smooth solution to the stationary Navier-Stokes system in $R^3$ with the velocity field, belonging globally to $L_6$ and $BM0^{-1}$, must be zero.