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


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 .


Weak Solution Sobolev Inequality Unbounded Domain Lipschitzian Domain Stokes Problem 
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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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