%0 Journal Article
%T A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion
%A Yoshikazu Giga
%A Pen-Yuan Hsu
%A Yasunori Maekawa
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1310.6471v1