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

Published online by Cambridge University Press:  17 February 2009

Chunshan Zhao  and
Kaitai Li
Chunshan Zhao
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA; e-mail: [email protected].
Kaitai Li
Affiliation:
School of Science, Xi'an Jiaotong University, Shaanxi, 710049, China; e-mail: [email protected].
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 1 , July 2004 , pp. 95 - 109
Copyright
Copyright © Australian Mathematical Society 2004

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