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


Pen-Yuan Hsu

14:20:00 - 15:10:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, 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. This is a joint work with Yoshikazu Giga (University of Tokyo) and Yasunori Maekawa (Tohoku University).