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.
Original language | English |
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Pages (from-to) | 1906-1935 |
Number of pages | 30 |
Journal | Communications in Partial Differential Equations |
Volume | 39 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2014 Oct |
Keywords
- Boundary conditions
- Geometric regularity criterion
- Liouville theorem
- Navier-Stokes equations
- Vorticity
- Vorticity equations
ASJC Scopus subject areas
- Analysis
- Applied Mathematics