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

Yoshikazu Giga, Pen Yuan Hsu, Yasunori Maekawa

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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 languageEnglish
Pages (from-to)1906-1935
Number of pages30
JournalCommunications in Partial Differential Equations
Volume39
Issue number10
DOIs
Publication statusPublished - 2014 Oct

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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