Nonhomogeneous boundary value problems for stationary navier-stokes equations in a multiply connected bounded domain

Hideo Kozono, Taku Yanagisawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider the stationary Navier-Stokes equations on a multiply connected bounded domain Ω in R{double-struck}n for n = 2; 3 under nonhomogeneous boundary conditions. We present a new sufficient condition for the existence of weak solutions. This condition is a variational estimate described in terms of the harmonic part of solenoidal extensions of the given boundary data; we prove it by using the Helmholtz-Weyl decomposition of vector fields over Ω satisfying adequate boundary conditions. We also study the validity of Leray's inequality for various assumptions about the symmetry of Ω.

Original languageEnglish
Pages (from-to)127-150
Number of pages24
JournalPacific Journal of Mathematics
Volume243
Issue number1
DOIs
Publication statusPublished - 2009 Nov 1

    Fingerprint

Keywords

  • Helmholtz-Weyl decomposition
  • Nonhomogeneous Boundary value problems
  • Stationary Navier-Stokes equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this