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arXiv · 1310.6471

A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion

Yoshikazu Giga·Pen-Yuan Hsu·Yasunori Maekawa
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Abstract

We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.

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Yoshikazu Giga, Pen-Yuan Hsu, Yasunori Maekawa. 2013-10-24. A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion. https://arxiv.org/abs/1310.6471

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