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

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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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Authors and Affiliations

  1. CEREMADE, Université Paris Dauphine, Paris, France

    Matthieu Hillairet

  2. Département de Physique Théorique, Université de Genève, Genève, Switzerland

    Peter Wittwer

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  1. Matthieu Hillairet
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  2. Peter Wittwer
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Correspondence to Matthieu Hillairet.

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Communicated by L. Saint-Raymond

Supported in part by the Swiss National Science Foundation.

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Hillairet, M., Wittwer, P. Asymptotic Description of Solutions of the Planar Exterior Navier–Stokes Problem in a Half Space. Arch Rational Mech Anal 205, 553–584 (2012). https://doi.org/10.1007/s00205-012-0515-6

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  • DOI: https://doi.org/10.1007/s00205-012-0515-6

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