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

Zhen Lei, Xiao Ren, Qi S. Zhang

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…