Well-posedness for mean-field evolutions arising in superconductivity Journal Article

Author(s): Duerinckx, Mitia; Fischer, Julian
Article Title: Well-posedness for mean-field evolutions arising in superconductivity
Affiliation IST 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 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.
Journal Title: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
ISSN: 0294-1449
Publisher: Elsevier  
Date Published: 2018-01-01
Start Page: Epub ahead of print
Sponsor: The work of the author is supported by F.R.S.-FNRS ( Fonds de la Recherche Scientifique - FNRS ) through a Research Fellowship.
DOI: 10.1016/j.anihpc.2017.11.004
Notes: The author would like to thank his PhD advisor Sylvia Serfaty as well as two anonymous referees for valuable comments and suggestions on this work.
Open access: yes (repository)
IST Austria Authors
  1. Julian Fischer
    17 Fischer
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