Ginzburg-Landau vortices : the static model
Tristan Rivière (1999-2000)
Séminaire Bourbaki
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Tristan Rivière (1999-2000)
Séminaire Bourbaki
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Yu N. Ovchinnikov, Israel Michael Sigal (1997-1998)
Séminaire Équations aux dérivées partielles
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We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture...
Sylvia Serfaty (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
Amandine Aftalion, Xavier Blanc (2008)
Annales de l'I.H.P. Analyse non linéaire
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Hassen Aydi, Etienne Sandier (2009)
Annales de l'I.H.P. Analyse non linéaire
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Yisong Yang (1994)
Annales de l'I.H.P. Analyse non linéaire
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El Mehdi, Khalil (2006)
Abstract and Applied Analysis
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