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arXiv · 1911.01571

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

Zhen Lei·Xiao Ren·Qi S. Zhang
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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.

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Zhen Lei, Xiao Ren, Qi S. Zhang. 2019-11-05. A Liouville Theorem for Axi-symmetric Navier-Stokes Equations on $\mathbb{R}^2 \times \mathbb{T}^1$. https://arxiv.org/abs/1911.01571

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