Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces

Weixi Li; Rui Xu; Tong Yang

doi:10.1007/s10473-022-0609-7

Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces

Weixi Li, Rui Xu, Tong Yang^*

^*Corresponding author for this work

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.

Original language	English
Pages (from-to)	2343–2366
Journal	Acta Mathematica Scientia
Volume	42
Issue number	6
Online published	3 Sept 2022
DOIs	https://doi.org/10.1007/s10473-022-0609-7
Publication status	Published - Nov 2022

Funding

W.-X. Li’s research was supported by NSF of China (11871054, 11961160716, 12131017) and the Natural Science Foundation of Hubei Province (2019CFA007). T. Yang’s research was supported by the General Research Fund of Hong Kong CityU (11304419).

Research Keywords

35M33
35Q35
76W05
auxiliary functions
Gevrey function space
global well-posedness
loss of derivative
magnetic Prandtl equation

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10.1007/s10473-022-0609-7

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title = "Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces",

abstract = "We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.",

keywords = "35M33, 35Q35, 76W05, auxiliary functions, Gevrey function space, global well-posedness, loss of derivative, magnetic Prandtl equation",

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T1 - Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces

AU - Li, Weixi

AU - Xu, Rui

AU - Yang, Tong

PY - 2022/11

Y1 - 2022/11

N2 - We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.

AB - We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.

KW - 35M33

KW - 35Q35

KW - 76W05

KW - auxiliary functions

KW - Gevrey function space

KW - global well-posedness

KW - loss of derivative

KW - magnetic Prandtl equation

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U2 - 10.1007/s10473-022-0609-7

DO - 10.1007/s10473-022-0609-7

M3 - RGC 21 - Publication in refereed journal

SN - 0252-9602

VL - 42

SP - 2343

EP - 2366

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 6

ER -

Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces

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GRF: Some Mathematical Theories for High Reynolds Number Limit

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Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces

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Funding

Research Keywords

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GRF: Some Mathematical Theories for High Reynolds Number Limit

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