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

Dongho Chae

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

Analysis of PDEs 2018-10-26 v2

Authors: Dongho Chae

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.

Keywords

navier-stokes equations liouville problem stationary solutions head pressure asymptotic formula

Cite

@article{arxiv.1810.09982,
  title  = {Notes on the Liouville type problem for the stationary Navier-Stokes equations in $\Bbb R^3$},
  author = {Dongho Chae},
  journal= {arXiv preprint arXiv:1810.09982},
  year   = {2018}
}

Comments

7 pages

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