A Liouville type theorem for axially symmetric $D$-solutions to steady Navier-Stokes Equations

Na Zhao

A Liouville type theorem for axially symmetric $D$-solutions to steady Navier-Stokes Equations

Analysis of PDEs 2018-08-27 v2

Authors: Na Zhao

Abstract

We study axially symmetric $D$ -solutions of three dimensional steady Navier-Stokes equations. We prove that if the velocity $u$ decays like $|x'|^{-(\frac{2}{3})^+}$ uniformly for $z$ , or the vorticity $\omega$ decays like $|x'|^{-(\frac{5}{3})^+}$ uniformly for $z$ , then $u$ vanishes. Here $|x'|$ denotes the distance to the axis.

Keywords

navier-stokes equations axially symmetric d-solutions liouville theorem vorticity decay velocity decay

Cite

@article{arxiv.1805.03845,
  title  = {A Liouville type theorem for axially symmetric $D$-solutions to steady Navier-Stokes Equations},
  author = {Na Zhao},
  journal= {arXiv preprint arXiv:1805.03845},
  year   = {2018}
}

Comments

15 pages, proof of Theorem 1.1 is updated

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