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Ill-posedness of the mean-field model of superconducting vortices and a possible regularisation

Published online by Cambridge University Press:  01 April 2000

G. RICHARDSON  and
B. STOTH
G. RICHARDSON
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
B. STOTH
Affiliation:
Mathematisches Institut, Universität Bonn, Bonn, Germany
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Abstract

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We conjecture that the mean-field model of superconducting vortices given in [10] is ill-posed wherever the electric current j has some component in the same direction as the vorticity vector ω (which gives the average density and direction of the superconducting vortices). The conjecture is illustrated with a linear stability analysis of a certain solution to the model. A regularised model is then proposed, and this is used to demonstrate the instability of force-free steady states in a certain geometry.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 2 , April 2000 , pp. 137 - 152
Copyright
2000 Cambridge University Press