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The limit states of magnetic relaxation

Published online by Cambridge University Press:  21 May 2007

MANUEL NÚÑEZ
MANUEL NÚÑEZ*
Affiliation:
Departamento de Análisis Matemático, Universidad de Valladolid, 47005 Valladolid, Spain e-mail: [email protected]
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Abstract

It is generally believed that a viscous, non-resistive plasma will eventually decay to a magnetostatic state, probably possessing contact discontinuities. We prove that even in the presence of a decaying forcing, the kinetic energy of the system tends to zero, which justifies the belief that the limit state is static. Regarding the magnetic field, the fact that the magnetic energy remains bounded proves the existence of weak sequential limits of the field as the time goes to infinity, but this does not imply that the magnetic field tends to a single state: we present an example where there is no limit, even in a weak sense. One additional condition upon the velocity, however, is enough to guarantee existence of a single limit magnetic configuration.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 580 , 10 June 2007 , pp. 251 - 260
Copyright
Copyright © Cambridge University Press 2007

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References

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