Well-posedness for mean-field evolutions arising in superconductivity |
| |
Authors: | Mitia Duerinckx Julian Fischer |
| |
Affiliation: | 1. Université Libre de Bruxelles (ULB), Brussels, Belgium;2. Laboratoire Jacques-Louis-Lions, Université Pierre et Marie Curie (UPMC), Paris, France;3. Institute of Science and Technology Austria (IST Austria), Klosterneuburg, Austria |
| |
Abstract: | We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in certain regimes in [24] 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. |
| |
Keywords: | with an appendix jointly written with |
本文献已被 ScienceDirect 等数据库收录! |
|