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Archive for Rational Mechanics and Analysis

, Volume 198, Issue 1, pp 331–348 | Cite as

A New Approach to the Existence of Weak Solutions of the Steady Navier–Stokes System with Inhomogeneous Boundary Data in Domains with Noncompact Boundaries

  • Jiří NeustupaEmail author
Article

Abstract

We prove the existence of a weak solution to the steady Navier–Stokes problem in a three dimensional domain Ω, whose boundary ∂Ω consists of M unbounded components Γ1, . . . , Γ M and NM bounded components ΓM+1, . . . , Γ N . We use the inhomogeneous Dirichlet boundary condition on ∂Ω. The prescribed velocity profile α on ∂Ω is assumed to have an L 3-extension to Ω with the gradient in L 2(Ω)3×3. We assume that the fluxes of α through the bounded components ΓM+1, . . . , Γ N of ∂Ω are “sufficiently small”, but we impose no restriction on the size of fluxes through the unbounded components Γ1, . . . , Γ M .

Keywords

Weak Solution Sobolev Inequality Unbounded Domain Lipschitzian Domain Stokes Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematical Institute of the Czech Academy of SciencesPraha 1Czech Republic

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