Well-posedness in Gevrey function spaces for the Prandtl equations with non-degenerate critical points

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)717-775
Journal / PublicationJournal of the European Mathematical Society
Volume22
Issue number3
Online published15 Nov 2019
Publication statusPublished - 2020

Abstract

We study the well-posedness of the Prandtl system without monotonicity and analyticity assumption. Precisely, for any index σ ∈ [3/2, 2], we obtain the local in time well-posedness in the space of Gevrey class Gσ in the tangential variable and Sobolev class in the normal variable so that the monotonicity condition on the tangential velocity is not needed to overcome the loss of tangential derivative. This answers an open question raised by D. Gérard-Varet and N. Masmoudi [Ann. Sci. École Norm. Sup. (4) 48 (2015), 1273-1325], who solved the case σ = 7/4.

Research Area(s)

  • Gevrey class, Non-degenerate critical points, Prandtl boundary layer