# Liouville properties of the Navier-Stokes​

2019-09-09 16:22

We establish a Liouville theorem for bounded ancient mild solutions to the axi-symmetric incompressible Navier-Stokes equations on $(-\infty, 0] \times (\mathbb{R}^2 \times \mathbb{T}^1)$. Connecting the compactness of $\mathbb{T}^1$ to the oscillation of the stream function is a crucial observation.