Well-posedness for mean-field evolutions arising in superconductivity
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.
Cite
@article{arxiv.1607.00268,
title = {Well-posedness for mean-field evolutions arising in superconductivity},
author = {Mitia Duerinckx},
journal= {arXiv preprint arXiv:1607.00268},
year = {2017}
}
Comments
53 pages; revised version, including an appendix jointly written with Julian Fischer about global existence for the degenerate parabolic case