Well-posedness of the Prandtl equations without any structural assumption

DOI10.1007/S40818-019-0063-6zbMATH Open1428.35355arXiv1809.11004OpenAlexW2892923032WikidataQ114687236 ScholiaQ114687236MaRDI QIDQ2273645

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Publication date: 24 September 2019

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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].

Full work available at URL: https://arxiv.org/abs/1809.11004

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Related Items (6)

Well-posedness for the Prandtl system without analyticity or monotonicity ⋮ Global well-posedness and finite time blowup of the Prandtl equation ⋮ Well-posedness in Gevrey function spaces for the Prandtl equations with non-degenerate critical points ⋮ Well-posed and stable problems for Prandtl's boundary layer system ⋮ Well-posedness of the generalized Proudman-Johnson equation without viscosity ⋮ Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

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