Well-posedness for mean-field evolutions arising in superconductivity

M. Duerinckx, J.L. Fischer, Annales de l’Institut Henri Poincare (C) Non Linear Analysis 35 (2018) 1267–1319.


Journal Article | Published | English
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;
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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 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.
Publishing Year
Date Published
2018-08-01
Journal Title
Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Acknowledgement
The work of the author is supported by F.R.S.-FNRS ( Fonds de la Recherche Scientifique - FNRS ) through a Research Fellowship.
Volume
35
Issue
5
Page
1267-1319
IST-REx-ID

Cite this

Duerinckx M, Fischer JL. Well-posedness for mean-field evolutions arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis. 2018;35(5):1267-1319. doi:10.1016/j.anihpc.2017.11.004
Duerinckx, M., & Fischer, J. L. (2018). Well-posedness for mean-field evolutions arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 35(5), 1267–1319. https://doi.org/10.1016/j.anihpc.2017.11.004
Duerinckx, Mitia, and Julian L Fischer. “Well-Posedness for Mean-Field Evolutions Arising in Superconductivity.” Annales de l’Institut Henri Poincare (C) Non Linear Analysis 35, no. 5 (2018): 1267–1319. https://doi.org/10.1016/j.anihpc.2017.11.004.
M. Duerinckx and J. L. Fischer, “Well-posedness for mean-field evolutions arising in superconductivity,” Annales de l’Institut Henri Poincare (C) Non Linear Analysis, vol. 35, no. 5, pp. 1267–1319, 2018.
Duerinckx M, Fischer JL. 2018. Well-posedness for mean-field evolutions arising in superconductivity. Annales de l’Institut Henri Poincare (C) Non Linear Analysis. 35(5), 1267–1319.
Duerinckx, Mitia, and Julian L. Fischer. “Well-Posedness for Mean-Field Evolutions Arising in Superconductivity.” Annales de l’Institut Henri Poincare (C) Non Linear Analysis, vol. 35, no. 5, Elsevier, 2018, pp. 1267–319, doi:10.1016/j.anihpc.2017.11.004.

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