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

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