Well-posedness of the Prandtl equation without any structural assumption

Helge Dietert; David Gerard-Varet

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arXiv · 1809.11004

Well-posedness of the Prandtl equation without any structural assumption

Helge Dietert·David Gerard-Varet

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Abstract

We show the local in time well-posedness of the Prandtl equation for data with Gevrey $2$ regularity in $x$ and $H^1$ regularity in $y$. The main novelty of our result is that we do not make any assumption on the structure of the initial data: no monotonicity or hypothesis on the critical points. Moreover, our general result is optimal in terms of regularity, in view of the ill-posedness result of [9].

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Helge Dietert, David Gerard-Varet. 2018-09-28. Well-posedness of the Prandtl equation without any structural assumption. https://arxiv.org/abs/1809.11004

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