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

Wei-Xi LI; Nader MASMOUDI; Tong YANG

doi:10.1002/cpa.21989

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

Wei-Xi LI^*, Nader MASMOUDI^*, Tong YANG

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

23 Citations (Scopus)

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. © 2021 Wiley Periodicals LLC.

Original language	English
Pages (from-to)	1755-1797
Journal	Communications on Pure and Applied Mathematics
Volume	75
Issue number	8
Online published	30 Mar 2021
DOIs	https://doi.org/10.1002/cpa.21989
Publication status	Published - Aug 2022

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title = "Well-Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption",

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. {\textcopyright} 2021 Wiley Periodicals LLC.",

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AU - LI, Wei-Xi

AU - MASMOUDI, Nader

AU - YANG, Tong

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Y1 - 2022/8

N2 - 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.

AB - 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.

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U2 - 10.1002/cpa.21989

DO - 10.1002/cpa.21989

M3 - RGC 21 - Publication in refereed journal

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EP - 1797

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 8

ER -

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

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GRF: Instability and Critical Regularity Indice for Degenerate PDEs of Prandtl-type Systems

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

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GRF: Instability and Critical Regularity Indice for Degenerate PDEs of Prandtl-type Systems

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