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

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 $r{u}_{\theta }$ 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.

22 pages

References in corpus (1)

• Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl