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

Wei Xi Li, Nader Masmoudi, Tong Yang

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
JournalCommunications on Pure and Applied Mathematics
DOIs
StateAccepted/In press - 2021

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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