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A mean-field model of superconducting vortices. (English) Zbl 0849.35135
Summary: A mean-field model for the motion of rectilinear vortices in the mixed state of a type-II superconductor is formulated. Steady-state solutions for some simple geometries are examined, and a local existence result is proved for an arbitrary smooth geometry. Finally, a variational formulation of the steady-state problem is given which shows the solution to be unique.

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
82D55 Statistical mechanics of superconductors
78A25 Electromagnetic theory (general)
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