Notes on the Liouville type problem for the stationary Navier-Stokes equations in ${\mathbb{R}}^3$

Abstract

In this paper we study the Liouville type problem for the stationary Navier-Stokes equations in ${\mathbb{R}}^3$. We deduce an asymptotic formula for an integral involving the head pressure, $Q=\frac{1}{2}|v{|}^2+p$, and its derivative over domains enclosed by level surfaces of $Q$. This formula provides us with new sufficient condition for the triviality of solution to the Navier-Stokes equations.

7 pages