2013
DOI: 10.1007/s00033-013-0304-6
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Existence of stationary solutions of the Navier–Stokes equations in the presence of a wall

Abstract: We consider the problem of a body moving within an incompressible ‡uid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible NavierStokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at in…nity. Here we prove existence of stationary solutions for this problem for the simpli…ed situation where the body is replaced by a source term of compact support.

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Cited by 3 publications
(12 citation statements)
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“…As in [10] we use throughout this paper a hat to indicate functions in Fourier space, i.e., we express functions f by:…”
Section: Preliminariesmentioning
confidence: 99%
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“…As in [10] we use throughout this paper a hat to indicate functions in Fourier space, i.e., we express functions f by:…”
Section: Preliminariesmentioning
confidence: 99%
“…Remark 3 Existence of solutions has been proved in [10] where we showed that ju i (x; y; z)j C=z 2 . Theorem 2 provides an explicit description of the dominant behavior of the velocity …eld and Theorem 1 implies that the bound in [10] is sharp for u 2 and u 3 , but not for u 1 :…”
Section: Introductionmentioning
confidence: 99%
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