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The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space

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Abstract

In their classical work, Sammartino and Caflisch (Commun Math Phys 192(2):433–461, 1998a; Commun Math Phys 192(2):463–491, 1998b) proved the inviscid limit of the incompressible Navier–Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl’s boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl’s boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy–Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.

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Authors and Affiliations

  1. Department of Mathematics, Penn State University, State College, PA, 16803, USA

    Toan T. Nguyen & Trinh T. Nguyen

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  1. Toan T. Nguyen
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  2. Trinh T. Nguyen
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Correspondence to Toan T. Nguyen.

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Communicated by P. Constantin

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Nguyen, T.T., Nguyen, T.T. The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space. Arch Rational Mech Anal 230, 1103–1129 (2018). https://doi.org/10.1007/s00205-018-1266-9

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  • DOI: https://doi.org/10.1007/s00205-018-1266-9

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