Well-posedness for mean-field evolutions arising in superconductivity
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1267-1319
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.
@article{AIHPC_2018__35_5_1267_0,
author = {Duerinckx, Mitia and Fischer, Julian},
title = {Well-posedness for mean-field evolutions arising in superconductivity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1267--1319},
year = {2018},
publisher = {Elsevier},
volume = {35},
number = {5},
doi = {10.1016/j.anihpc.2017.11.004},
mrnumber = {3813965},
zbl = {1393.35230},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.11.004/}
}
TY - JOUR AU - Duerinckx, Mitia AU - Fischer, Julian TI - Well-posedness for mean-field evolutions arising in superconductivity JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 1267 EP - 1319 VL - 35 IS - 5 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.11.004/ DO - 10.1016/j.anihpc.2017.11.004 LA - en ID - AIHPC_2018__35_5_1267_0 ER -
%0 Journal Article %A Duerinckx, Mitia %A Fischer, Julian %T Well-posedness for mean-field evolutions arising in superconductivity %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 1267-1319 %V 35 %N 5 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.11.004/ %R 10.1016/j.anihpc.2017.11.004 %G en %F AIHPC_2018__35_5_1267_0
Duerinckx, Mitia; Fischer, Julian. Well-posedness for mean-field evolutions arising in superconductivity. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1267-1319. doi: 10.1016/j.anihpc.2017.11.004
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