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arXiv · 1305.0221

Well-posedness for the Prandtl system without analyticity or monotonicity

Davdi Gerard-Varet·Nader Masmoudi
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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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Davdi Gerard-Varet, Nader Masmoudi. 2013-05-01. Well-posedness for the Prandtl system without analyticity or monotonicity. https://arxiv.org/abs/1305.0221

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