Spatial decay bounds in a linearized magnetohydrodynamic channel flow

Julie Lee; J. C. Song

doi:10.3934/cpaa.2013.12.1349

Article Contents

2013, Volume 12, Issue 3: 1349-1361. Doi: 10.3934/cpaa.2013.12.1349

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Spatial decay bounds in a linearized magnetohydrodynamic channel flow

Julie Lee^1, and
J. C. Song^2,

1.
Chung-Ang University, Heuksuk-Dong, Donggak-Gu, 156-756
2.
Hanyang University, Ansan, Gyeonggido 426-791

Received: March 31, 2012

Revised: June 30, 2012

Published: April 2013

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Abstract

This paper establishes exponential decay bounds for a transient magnetohydrodynamic flow in a semi-infinite channel. If net entrance flows into the channel are nonzero, then the solutions will not tend to zero as the distance from the entrance end tends to infinity when homogeneous lateral surface boundary conditions and homogenous initial conditions are applied. Assuming that the entrance data are small enough so that flows converge to transient laminar flows as the distance from the entrance section tends to infinity, we linearize the magnetohydrodynamic equations and derive an integro-differential inequality that leads to an exponential decay estimate. This paper also indicates how to bound the total energy in the spirit of earlier work of Lin and Payne [11].

Keywords:

Magnetohydrodynamic equations,
spatial decay bounds.

Mathematics Subject Classification: Primary: 35B45, 35K55; Secondary: 76W05.

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References

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