Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay

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

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Original languageEnglish
Pages (from-to)150-162
Journal / PublicationJournal des Mathematiques Pures et Appliquees
Issue number2
Online published2 Nov 2016
Publication statusPublished - Aug 2017


Motivated by the paper Gérard-Varet and Dormy (2010) [6] [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations in Sobolev spaces, this paper aims to extend the result in [6] to the case when the shear flow has general decay. The key observation is to construct an approximate solution that captures the initial layer to the linearized problem motivated by the precise formulation of solutions to the inviscid Prandtl equations.

Research Area(s)

  • General decay, Linear instability, Prandtl equations, Shear flow