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On a model of rotating superfluids

Published online by Cambridge University Press:  15 August 2002

Sylvia Serfaty
Sylvia Serfaty*
Affiliation:
CMLA, École Normale Supérieure de Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex, France; serfaty@cmla.ens-cachan.fr.
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Abstract

We consider an energy-functional describing rotating superfluids at a rotating velocity ω, 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 ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.

Keywords

VorticesGross-Pitaevskii equationssuperfluids.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 201 - 238
Copyright
© EDP Sciences, SMAI, 2001

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References

Almeida, L. and Bethuel, F., Topological Methods for the Ginzburg-Landau Equations. J. Math. Pures Appl. 77 (1998) 1-49. CrossRef
A. Aftalion (in preparation.)
A. Aftalion, E. Sandier and S. Serfaty, Pinning Phenomena in the Ginzburg-Landau Model of Superconductivity. J. Math. Pures Appl. (to appear).
N. André and I. Shafrir, Minimization of a Ginzburg-Landau type functional with nonvanishing Dirichlet boundary condition. Calc. Var. Partial Differential Equations (1998) 1-27.
F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices. Birkhäuser (1994).
Bonnet, A. and Monneau, R., Distribution of vortices in a type-II superconductor as a free boundary problem: Existence and regularity via Nash-Moser theory. Interfaces Free Bound. 2 (2000) 181-200. CrossRef
Brezis, H. and Oswald, L., Remarks on sublinear elliptic equations. Nonlinear Anal. 10 (1986) 55-64. CrossRef
Butts, D.A. and Rokhsar, D.S., Predicted signatures of rotating Bose-Einstein condensates. Nature 397 (1999) 327-329.
Castin, Y. and Dum, R., Bose-Einstein condensates with vortices in rotating traps. Eur. Phys. J. D 7 (1999) 399-412. CrossRef
A. Fetter, Vortices and Ions in Helium, in The physics of liquid and solid helium, part I, edited by K.H. Bennemann and J.B. Keterson. John Wiley, Interscience, Interscience Monographs and Texts in Physics and Astronomy 30 (1976).
Gueron, S. and Shafrir, I., On a Discrete Variational Problem Involving Interacting Particles. SIAM J. Appl. Math. 60 (2000) 1-17. CrossRef
D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Acad. Press (1980).
Lassoued, L. and Mironescu, P., Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math. 77 (1999) 1-26. CrossRef
Owen, N., Rubinstein, J. and Sternberg, P., Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition. Proc. Roy. Soc. London Ser. A 429 (1990) 503-532. CrossRef
J.F. Rodrigues, Obstacle Problems in Mathematical Physics. Mathematical Studies, North Holland (1987).
Serfaty, S., Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part I. Comm. Contemporary Math. 1 (1999) 213-254. CrossRef
Serfaty, S., Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part II. Comm. Contemporary Math. 1 (1999) 295-333. CrossRef
Serfaty, S., Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation. Arch. Rational Mech. Anal. 149 (1999) 329-365. CrossRef
S. Serfaty, Sur l'équation de Ginzburg-Landau avec champ magnétique, in Proc. of Journées Équations aux dérivées partielles, Saint-Jean-de-Monts (1998).
Sandier, E. and Serfaty, S., Global Minimizers for the Ginzburg-Landau Functional below the First Critical Magnetic Field. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 119-145. CrossRef
E. Sandier and S. Serfaty, On the Energy of Type-II Superconductors in the Mixed Phase. Rev. Math. Phys. (to appear).
Sandier, E. and Serfaty, S., Rigorous Der, Aivation of a Free-Boundary Problem Arising in Superconductivity. Annales Sci. École Norm. Sup. (4) 33 (2000) 561-592. CrossRef
E. Sandier and S. Serfaty, Ginzburg-Landau Minimizers Near the First Critical Field Have Bounded Vorticity. Preprint.
D. Tilley and J. Tilley, Superfluidity and Superconductivity, 2nd edition. Adam Hilger Ltd., Bristol (1986).