Archive for Rational Mechanics and Analysis

, Volume 205, Issue 2, pp 553–584 | Cite as

Asymptotic Description of Solutions of the Planar Exterior Navier–Stokes Problem in a Half Space

Article

Abstract

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall in an otherwise unbounded domain. This situation is modeled by the incompressible Navier–Stokes equations in a planar exterior domain in a half space with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall.

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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.CEREMADE, Université Paris DauphineParisFrance
  2. 2.Département de Physique ThéoriqueUniversité de GenèveGenèveSwitzerland

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