Remarks on the ill-posedness of the Prandtl equation

D. Gérard-Varet, T. Nguyen

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

In the lines of the recent paper [J. Amer. Math. Soc. 23(2) (2010), 591-609], we establish various ill-posedness results for the Prandtl equation. By considering perturbations of stationary non-monotonic shear flows, we show that for some C initial data, local in time H 1 solutions of the linearized Prandtl equation do not exist. At the nonlinear level, we prove that if a flow exists in the Sobolev setting, it cannot be Lipschitz continuous. Besides ill-posedness in time, we also establish some ill-posedness in space, that casts some light on the results obtained by Oleinik for monotonic data.

Original languageEnglish (US)
Pages (from-to)71-88
Number of pages18
JournalAsymptotic Analysis
Volume77
Issue number1-2
DOIs
StatePublished - Apr 11 2012

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Ill-posedness
Shear Flow
Monotonic
Lipschitz
Perturbation
Line

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Gérard-Varet, D. ; Nguyen, T. / Remarks on the ill-posedness of the Prandtl equation. In: Asymptotic Analysis. 2012 ; Vol. 77, No. 1-2. pp. 71-88.
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Remarks on the ill-posedness of the Prandtl equation. / Gérard-Varet, D.; Nguyen, T.

In: Asymptotic Analysis, Vol. 77, No. 1-2, 11.04.2012, p. 71-88.

Research output: Contribution to journalArticle

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