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arXiv · 1501.02412

On Liouville Type of Theorems to the 3-D Incompressible Axisymmetric Navier-Stokes Equations

Quansen Jiu·Zhouping Xin
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Abstract

Liouville type of theorems play a key role in the blow-up approach to study the global regularity of the three-dimensional Navier-Stokes equations. In this paper, we will prove Liouville type of theorems to the 3-D axisymmetric Navier-Stokes equations with swirls under some suitable assumptions on swirl component velocity $u_\theta$ which are scaling invariant. It is known that $ru_\theta$ satisfies the maximum principle. The assumptions on $u_\theta$ will be natural and useful to make further studies on the global regularity to the three-dimensional incompressible axisymmetric Navier-Stokes equations.

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Quansen Jiu, Zhouping Xin. 2015-01-11. On Liouville Type of Theorems to the 3-D Incompressible Axisymmetric Navier-Stokes Equations. https://arxiv.org/abs/1501.02412

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