Well-Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1755-1797
Journal / PublicationCommunications on Pure and Applied Mathematics
Issue number8
Online published30 Mar 2021
Publication statusPublished - Aug 2022


We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three-dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three-dimensional instabilities in the system leading to ill-posedness are not worse than the two-dimensional ones. © 2021 Wiley Periodicals LLC.