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

Hideo Kozono, Taku Yanagisawa

Research output: Contribution to journalArticle

3 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
Externally publishedYes

Fingerprint

Stationary Navier-Stokes Equations
Multiply Connected Domain
Nonhomogeneous Boundary Conditions
Existence of Weak Solutions
Hermann Von Helmholtz
Bounded Domain
Vector Field
Harmonic
Boundary Value Problem
Boundary conditions
Symmetry
Decompose
Sufficient Conditions
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonhomogeneous boundary value problems for stationary navier-stokes equations in a multiply connected bounded domain. / Kozono, Hideo; Yanagisawa, Taku.

In: Pacific Journal of Mathematics, Vol. 243, No. 1, 11.2009, p. 127-150.

Research output: Contribution to journalArticle

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