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

Dongho Chae

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arXiv · 1810.09982

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

Dongho Chae

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Abstract

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.

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Dongho Chae. 2018-10-23. Notes on the Liouville type problem for the stationary Navier-Stokes equations in $\Bbb R^3$. https://arxiv.org/abs/1810.09982

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