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Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations

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Abstract

We study the inviscid limit of the free boundary Navier–Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a strong compactness argument to justify the inviscid limit. Our approach does not rely on the justification of asymptotic expansions. In particular, we get a new existence result for the Euler equations with free surface from the one for Navier–Stokes.

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Authors and Affiliations

  1. Courant Institute, 251 Mercer Street, New York, NY, 10012-1185, USA

    Nader Masmoudi

  2. Laboratoire de Mathématiques d’Orsay, Université Paris-Sud et IUF, 91405, Orsay Cedex, France

    Frederic Rousset

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  1. Nader Masmoudi
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  2. Frederic Rousset
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Correspondence to Nader Masmoudi.

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Communicated by C. Le Bris

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Masmoudi, N., Rousset, F. Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations. Arch Rational Mech Anal 223, 301–417 (2017). https://doi.org/10.1007/s00205-016-1036-5

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