A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion

作者：Giga Yoshikazu; Hsu Pen Yuan; Maekawa Yasunori^*

来源：Communications in Partial Differential Equations, 2014, 39(10): 1906-1935.

DOI：10.1080/03605302.2014.912662

• Boundary conditions
• Geometric regularity criterion
• Liouville theorem
• Navier-Stokes equations
• Vorticity
• Vorticity equations

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.

• 出版日期2014