JUSTIFICATION OF PRANDTL ANSATZ FOR MHD BOUNDARY LAYER

Cheng-Jie LIU; Feng XIE; Tong YANG

doi:10.1137/18M1219618

JUSTIFICATION OF PRANDTL ANSATZ FOR MHD BOUNDARY LAYER

Cheng-Jie LIU, Feng XIE, Tong YANG

Department of Mathematics

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

54 Citations (Scopus)

33 Downloads (CityUHK Scholars)

Abstract

The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on a velocity field and perfectly conducting wall condition on a magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give an L^∞estimate on the error by multiscale analysis.

Original language	English
Pages (from-to)	2748-2791
Journal	SIAM Journal on Mathematical Analysis
Volume	51
Issue number	3
Online published	27 Jun 2019
DOIs	https://doi.org/10.1137/18M1219618
Publication status	Published - 2019

Research Keywords

MHD boundary layer
high Reynolds numbers limit
Prandtl boundary layer expansion
L-infinity estimate
GLOBAL SMALL SOLUTIONS
NAVIER-STOKES EQUATION
ZERO VISCOSITY LIMIT
WELL-POSEDNESS
ILL-POSEDNESS
ANALYTIC SOLUTIONS
SOBOLEV SPACES
HALF-SPACE
EXISTENCE
SYSTEM

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2019 Society for Industrial and Applied Mathematics.

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10.1137/18M1219618

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title = "JUSTIFICATION OF PRANDTL ANSATZ FOR MHD BOUNDARY LAYER",

abstract = "The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on a velocity field and perfectly conducting wall condition on a magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give an L∞ estimate on the error by multiscale analysis.",

keywords = "MHD boundary layer, high Reynolds numbers limit, Prandtl boundary layer expansion, L-infinity estimate, GLOBAL SMALL SOLUTIONS, NAVIER-STOKES EQUATION, ZERO VISCOSITY LIMIT, WELL-POSEDNESS, ILL-POSEDNESS, ANALYTIC SOLUTIONS, SOBOLEV SPACES, HALF-SPACE, EXISTENCE, SYSTEM",

author = "Cheng-Jie LIU and Feng XIE and Tong YANG",

year = "2019",

doi = "10.1137/18M1219618",

language = "English",

volume = "51",

pages = "2748--2791",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics",

number = "3",

}

TY - JOUR

T1 - JUSTIFICATION OF PRANDTL ANSATZ FOR MHD BOUNDARY LAYER

AU - LIU, Cheng-Jie

AU - XIE, Feng

AU - YANG, Tong

PY - 2019

Y1 - 2019

N2 - The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on a velocity field and perfectly conducting wall condition on a magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give an L∞ estimate on the error by multiscale analysis.

AB - The paper aims to justify the high Reynolds numbers limit for the magnetohydrodynamics system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on a velocity field and perfectly conducting wall condition on a magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give an L∞ estimate on the error by multiscale analysis.

KW - MHD boundary layer

KW - high Reynolds numbers limit

KW - Prandtl boundary layer expansion

KW - L-infinity estimate

KW - GLOBAL SMALL SOLUTIONS

KW - NAVIER-STOKES EQUATION

KW - ZERO VISCOSITY LIMIT

KW - WELL-POSEDNESS

KW - ILL-POSEDNESS

KW - ANALYTIC SOLUTIONS

KW - SOBOLEV SPACES

KW - HALF-SPACE

KW - EXISTENCE

KW - SYSTEM

UR - http://www.scopus.com/inward/record.url?scp=85069156824&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85069156824&origin=recordpage

U2 - 10.1137/18M1219618

DO - 10.1137/18M1219618

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1410

VL - 51

SP - 2748

EP - 2791

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

JUSTIFICATION OF PRANDTL ANSATZ FOR MHD BOUNDARY LAYER

Abstract

Research Keywords

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GRF: Stability and Instability Analysis of Compressible Fluid with non-slip Boundary Condition

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JUSTIFICATION OF PRANDTL ANSATZ FOR MHD BOUNDARY LAYER

Abstract

Research Keywords

Publisher's Copyright Statement

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Permanent Link

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GRF: Stability and Instability Analysis of Compressible Fluid with non-slip Boundary Condition

Cite this