ANZIAM  J.  46 (2004), 95-109
On existence, uniqueness and $L^r$-exponential stability for stationary solutions to the MHD equations in three-dimensional domains

Chunshan Zhao
  Department of Mathematics
  The University of Iowa
  Iowa City, IA 52242
  USA
    chuzhao@math.uiowa.edu
and
Kaitai Li
  School of Science
  Xi'an Jiaotong University
  Shaanxi 710049
  China
    ktli@mail.xjtu.edu.cn


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 $L^2$ and $L^r$ norms exponentially as time goes to infinity.
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