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Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition

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Abstract

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier–Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L ∞. This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

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Authors and Affiliations

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

    Nader Masmoudi

  2. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes cedex, France

    Frédéric Rousset

Authors
  1. Nader Masmoudi
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  2. Frédéric Rousset
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Correspondence to Nader Masmoudi.

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Communicated by C. Dafermos

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Masmoudi, N., Rousset, F. Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition. Arch Rational Mech Anal 203, 529–575 (2012). https://doi.org/10.1007/s00205-011-0456-5

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  • DOI: https://doi.org/10.1007/s00205-011-0456-5

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