A Liouville Theorem for the Planer Navier-Stokes Equations with the No-Slip Boundary Condition and Its Application to a Geometric Regularity Criterion |
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Authors: | Yoshikazu Giga Pen-Yuan Hsu |
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Affiliation: | 1. Graduate School of Mathematical Sciences , University of Tokyo , Tokyo , Japan;2. Department of Mathematics , Waseda University , Tokyo , Japan |
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Abstract: | 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. |
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Keywords: | Boundary conditions Geometric regularity criterion Liouville theorem Navier-Stokes equations Vorticity Vorticity equations |
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