Well-posedness for mean-field evolutions arising in superconductivity
Résumé
We establish the existence of a global solution to a family of equations, which are obtained in certain regimes in [19] as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution.
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