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(2005 / vol.8 / no.2)
Decay bounds for magnetohydrodynamic geophysical Flow
J.C. Song
Pages. 37-42     



This paper establishes exponential decay bounds for steady
magnetohydrodynamic geophysical pipe flow
when homogeneous lateral surface boundary
conditions are applied. In the spirit
of earlier work of Horgan and Wheeler~(SIAM J. Appl. Math. 35 (1978) 789)
and Ames and Payne~(SIAM J.
Math. Anal. 20 (1989) 97), the decay to fully developed flow as a function of
distance from the entry
section is investigated. Here, it is not assumed that the flow is fully
developed at the exit section. Energy inequalities are derived that lead to
estimates for the ``energy'' associated with the velocity and magnetic
field
represented by the difference between the entrance flow and the fully
developed flow in a portion of the pipe near the exit section. This
paper also indicates how to bound the total energy.



1. Introduction
2. Formulation of problem
3. Decay estimates