A Liouville Theorem for Axi-symmetric Navier-Stokes Equations on $\mathbb{R}^2 \times \mathbb{T}^1$

Zhen Lei; Xiao Ren; Qi S. Zhang

A Liouville Theorem for Axi-symmetric Navier-Stokes Equations on $\mathbb{R}^2 \times \mathbb{T}^1$

Analysis of PDEs 2019-11-06 v1

Authors: Zhen Lei , Xiao Ren , Qi S. Zhang

Abstract

We establish a Liouville theorem for bounded mild ancient solutions to the axi-symmetric incompressible Navier-Stokes equations on $(-\infty, 0] \times (\mathbb{R}^2 \times \mathbb{T}^1)$ . This is a step forward to completely solve the conjecture on $(-\infty, 0] \times \mathbb{R}^3$ which was made in \cite{KNSS} to describe the potential singularity structures of the Cauchy problem.

Keywords

liouville theorem navier-stokes equations axi-symmetric mild ancient solutions singularity

Cite

@article{arxiv.1911.01571,
  title  = {A Liouville Theorem for Axi-symmetric Navier-Stokes Equations on $\mathbb{R}^2 \times \mathbb{T}^1$},
  author = {Zhen Lei and Xiao Ren and Qi S. Zhang},
  journal= {arXiv preprint arXiv:1911.01571},
  year   = {2019}
}

Related papers

View all related →