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Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

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Abstract

The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be \({O(\sqrt{\nu})}\). The main assumption is spatial analyticity of the initial datum.

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Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    Igor Kukavica

  2. Department of Mathematics, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Maria Carmela Lombardo & Marco Sammartino

Authors
  1. Igor Kukavica
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  2. Maria Carmela Lombardo
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  3. Marco Sammartino
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Correspondence to Igor Kukavica.

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Communicated by P. Constantin

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Kukavica, I., Lombardo, M.C. & Sammartino, M. Zero Viscosity Limit for Analytic Solutions of the Primitive Equations. Arch Rational Mech Anal 222, 15–45 (2016). https://doi.org/10.1007/s00205-016-0995-x

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  • DOI: https://doi.org/10.1007/s00205-016-0995-x

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