Well-posedness for mean-field evolutions arising in superconductivity

Mitia Duerinckx

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arXiv · 1607.00268

Well-posedness for mean-field evolutions arising in superconductivity

Mitia Duerinckx

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Abstract

We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in a joint work with Serfaty in certain regimes 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. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data.

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Mitia Duerinckx. 2016-07-01. Well-posedness for mean-field evolutions arising in superconductivity. https://arxiv.org/abs/1607.00268

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