Well-posedness for the Prandtl system without analyticity or monotonicity

David Gérard-Varet, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

It has been thought for a while that the Prandtl system is only well-posed under the Oleinik monotonicity assumption or under an analyticity assumption. We show that the Prandtl system is actually locally well-posed for data that belong to the Gevrey class 7/4 in the horizontal variable x. Our result improves the classical local well-posedness result for data that are analytic in x (that is Gevrey class 1). The proof uses new estimates, based on non-quadratic energy functionals.

Original languageEnglish (US)
Pages (from-to)1273-1325
Number of pages53
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume48
Issue number6
StatePublished - Nov 1 2015

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Gevrey Classes
Analyticity
Well-posedness
Monotonicity
Local Well-posedness
Horizontal
Energy
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Well-posedness for the Prandtl system without analyticity or monotonicity. / Gérard-Varet, David; Masmoudi, Nader.

In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 48, No. 6, 01.11.2015, p. 1273-1325.

Research output: Contribution to journalArticle

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