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

Hideo Kozono, Taku Yanagisawa

研究成果: Article

3 引用 (Scopus)

抄録

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.

元の言語English
ページ(範囲)127-150
ページ数24
ジャーナルPacific Journal of Mathematics
243
発行部数1
DOI
出版物ステータスPublished - 2009 11
外部発表Yes

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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

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

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AB - 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.

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