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arXiv · 2103.11200

Long-time asymptotics of $3$-D axisymmetric Navier-Stokes equations in critical spaces

Yanlin Liu
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Abstract

We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces must eventually become a small solution. In particular, we show that the limits of $\|\omega^\theta(t)/r\|_{L^1}$ and $\|u^\theta(t)/\sqrt r\|_{L^2}$ are all $0$ as $t$ tends to infinity. And by using this, we can refine some decay estimates for the axisymmetric solutions.

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Yanlin Liu. 2021-03-20. Long-time asymptotics of $3$-D axisymmetric Navier-Stokes equations in critical spaces. https://arxiv.org/abs/2103.11200

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