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Almost Global Existence for the Prandtl Boundary Layer Equations

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Abstract

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H 1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within \({\varepsilon}\) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time \({T_{\varepsilon} \geqq {\rm exp}(\varepsilon^{-1} / {\rm log}(\varepsilon^{-1}))}\).

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Mihaela Ignatova & Vlad Vicol

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  1. Mihaela Ignatova
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  2. Vlad Vicol
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Correspondence to Mihaela Ignatova.

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Communicated by P. Constantin

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Ignatova, M., Vicol, V. Almost Global Existence for the Prandtl Boundary Layer Equations. Arch Rational Mech Anal 220, 809–848 (2016). https://doi.org/10.1007/s00205-015-0942-2

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  • DOI: https://doi.org/10.1007/s00205-015-0942-2

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