  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.
