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

Dongho Chae

Published 2018-10-23Version 1

In this paper we study the Liouville type problem for the stationary Navier-Stokes equations in $\Bbb R^3$. We deduce an asymptotic formula for an integral involving the head pressure, $Q=\frac12 |v|^2 +p$, 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. We also present an alternative proof of the Liouville type theorem due to Seregin.