On existence, uniqueness and Lr-exponential stability for stationary solutions to the MHD equations in three-dimensional domains

Chunshan Zhao; Kaitai Li

doi:10.1017/S1446181100013705

On existence, uniqueness and L^r-exponential stability for stationary solutions to the MHD equations in three-dimensional domains

Chunshan Zhao
, Kaitai Li

Mathematical Sciences

University of Iowa
Xi'an Jiaotong University

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any L^r (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L² and L^r norms exponentially as time goes to infinity.

Original language	English
Pages (from-to)	95-109
Number of pages	15
Journal	ANZIAM Journal
Volume	46
Issue number	1
DOIs	https://doi.org/10.1017/S1446181100013705
State	Published - Jul 2004

Scopus Subject Areas

Mathematics (miscellaneous)

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10.1017/S1446181100013705

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title = "On existence, uniqueness and Lr-exponential stability for stationary solutions to the MHD equations in three-dimensional domains",

abstract = "The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any Lr (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L2 and Lr norms exponentially as time goes to infinity.",

author = "Chunshan Zhao and Kaitai Li",

note = "The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any L r (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L 2 and L r norms exponentially as time goes to infinity.",

year = "2004",

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T1 - On existence, uniqueness and Lr-exponential stability for stationary solutions to the MHD equations in three-dimensional domains

AU - Zhao, Chunshan

AU - Li, Kaitai

N1 - The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any L r (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L 2 and L r norms exponentially as time goes to infinity.

PY - 2004/7

Y1 - 2004/7

N2 - The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any Lr (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L2 and Lr norms exponentially as time goes to infinity.

AB - The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any Lr (r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L2 and Lr norms exponentially as time goes to infinity.

UR - https://www.scopus.com/pages/publications/33747339961

U2 - 10.1017/S1446181100013705

DO - 10.1017/S1446181100013705

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JO - ANZIAM Journal

JF - ANZIAM Journal

IS - 1

ER -

On existence, uniqueness and L^r-exponential stability for stationary solutions to the MHD equations in three-dimensional domains

Abstract

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