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

2013/10/23 by Yoshikazu Giga, Giga, Yoshikazu, Pen-Yuan Hsu +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1310.6471

Abstract

We establish a Liouville type result for a backward global solution to the\nNavier-Stokes equations in the half plane with the no-slip boundary condition.\nNo assumptions on spatial decay for the vorticity nor the velocity field are\nimposed. We study the vorticity equations instead of the original Navier-Stokes\nequations. As an application, we extend the geometric regularity criterion for\nthe Navier-Stokes equations in the three-dimensional half space under the\nno-slip boundary condition.\n

Citations

• Liouville theorems for the Navier–Stokes equations and applications

Related

• Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components
• On the extension to slip boundary conditions of a Bae and Choe regularity criterion for the Navier-Stokes equations. The half-space case
• Liouville type theorems for stationary Navier-Stokes equations
• Liouville Theorem for 2D Navier-Stokes equations in Half Space
• Remark on Wolf's condition for boundary regularity of Navier-Stokes equations