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

2015/01/11 by Jiu, Quansen, Xin, Zhouping
#35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.02412

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_θ which are scaling invariant. It is known that ru_θ satisfies the maximum principle. The assumptions on u_θ will be natural and useful to make further studies on the global regularity to the three-dimensional incompressible axisymmetric Navier-Stokes equations.

Related

• Muliti-scale regularity of axisymmetric Navier-Stokes equations
• Regularity of 3D axisymmetric Navier-Stokes equations
• Global smooth axisymmetric solutions of 3-D Inhomogenenous incompressible Navier-Stokes system
• Remarks on Liouville type theorems for the 3D steady axially symmetric Navier-Stokes equations
• A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations