Well-posedness for the Prandtl system without analyticity or monotonicity

David Gérard-Varet; Nader Masmoudi

doi:10.24033/asens.2270

Well-posedness for the Prandtl system without analyticity or monotonicity

David Gérard-Varet, Nader Masmoudi

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1273-1325
Number of pages	53
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	48
Issue number	6
DOIs	https://doi.org/10.24033/asens.2270
State	Published - Nov 1 2015

ASJC Scopus subject areas

General Mathematics

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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.",

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Well-posedness for the Prandtl system without analyticity or monotonicity

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