WELL-POSEDNESS OF THE MHD BOUNDARY LAYER SYSTEM IN GEVREY FUNCTION SPACE WITHOUT STRUCTURAL ASSUMPTION

Wei-Xi LI; Tong YANG

doi:10.1137/20M1367027

WELL-POSEDNESS OF THE MHD BOUNDARY LAYER SYSTEM IN GEVREY FUNCTION SPACE WITHOUT STRUCTURAL ASSUMPTION

Wei-Xi LI, Tong YANG

Department of Mathematics

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

17 Citations (Scopus)

54 Downloads (CityUHK Scholars)

Abstract

We establish the well-posedness of the MHD boundary layer system in Gevrey function space without any structural assumption. Compared to the classical Prandtl equation, the loss of tangential derivative comes from both the velocity and magnetic fields that are coupled with each other. By observing a new type of cancellation mechanism in the system for overcoming the loss derivative degeneracy, we show that the MHD boundary layer system is well-posed with Gevrey index up to 3/2 in both two- and three-dimensional spaces.

Original language	English
Pages (from-to)	3236-3264
Journal	SIAM Journal on Mathematical Analysis
Volume	53
Issue number	3
Online published	10 Jun 2021
DOIs	https://doi.org/10.1137/20M1367027
Publication status	Published - 2021

Research Keywords

Cancellation
Gevrey class
MHD boundary layer
Nonstructural assumption
Well-posedness theory

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COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2021 Society for Industrial and Applied Mathematics.

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10.1137/20M1367027

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author = "Wei-Xi LI and Tong YANG",

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language = "English",

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AU - LI, Wei-Xi

AU - YANG, Tong

PY - 2021

Y1 - 2021

N2 - We establish the well-posedness of the MHD boundary layer system in Gevrey function space without any structural assumption. Compared to the classical Prandtl equation, the loss of tangential derivative comes from both the velocity and magnetic fields that are coupled with each other. By observing a new type of cancellation mechanism in the system for overcoming the loss derivative degeneracy, we show that the MHD boundary layer system is well-posed with Gevrey index up to 3/2 in both two- and three-dimensional spaces.

AB - We establish the well-posedness of the MHD boundary layer system in Gevrey function space without any structural assumption. Compared to the classical Prandtl equation, the loss of tangential derivative comes from both the velocity and magnetic fields that are coupled with each other. By observing a new type of cancellation mechanism in the system for overcoming the loss derivative degeneracy, we show that the MHD boundary layer system is well-posed with Gevrey index up to 3/2 in both two- and three-dimensional spaces.

KW - Cancellation

KW - Gevrey class

KW - MHD boundary layer

KW - Nonstructural assumption

KW - Well-posedness theory

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DO - 10.1137/20M1367027

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1410

VL - 53

SP - 3236

EP - 3264

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

WELL-POSEDNESS OF THE MHD BOUNDARY LAYER SYSTEM IN GEVREY FUNCTION SPACE WITHOUT STRUCTURAL ASSUMPTION

Abstract

Research Keywords

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GRF: Some Mathematical Theories for High Reynolds Number Limit

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WELL-POSEDNESS OF THE MHD BOUNDARY LAYER SYSTEM IN GEVREY FUNCTION SPACE WITHOUT STRUCTURAL ASSUMPTION

Abstract

Research Keywords

Publisher's Copyright Statement

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GRF: Some Mathematical Theories for High Reynolds Number Limit

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