On a model of rotating superfluids
ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 201-238.

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

Classification : 35Q99,  35J60,  35J50,  35B40,  35B25
Mots clés : vortices, Gross-Pitaevskii equations, superfluids
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Serfaty, Sylvia. On a model of rotating superfluids. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 201-238. http://www.numdam.org/item/COCV_2001__6__201_0/

[1] L. Almeida and F. Bethuel, Topological Methods for the Ginzburg-Landau Equations. J. Math. Pures Appl. 77 (1998) 1-49. | Zbl 0904.35023

[2] A. Aftalion (in preparation.)

[3] A. Aftalion, E. Sandier and S. Serfaty, Pinning Phenomena in the Ginzburg-Landau Model of Superconductivity. J. Math. Pures Appl. (to appear). | MR 1826348 | Zbl 1027.35123

[4] 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. | Zbl 0910.49001

[5] F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices. Birkhäuser (1994). | MR 1269538 | Zbl 0802.35142

[6] A. Bonnet and R. Monneau, 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. | Zbl 0989.35146

[7] H. Brezis and L. Oswald, Remarks on sublinear elliptic equations. Nonlinear Anal. 10 (1986) 55-64. | Zbl 0593.35045

[8] D.A. Butts and D.S. Rokhsar, Predicted signatures of rotating Bose-Einstein condensates. Nature 397 (1999) 327-329.

[9] Y. Castin and R. Dum, Bose-Einstein condensates with vortices in rotating traps. Eur. Phys. J. D 7 (1999) 399-412.

[10] 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).

[11] S. Gueron and I. Shafrir, On a Discrete Variational Problem Involving Interacting Particles. SIAM J. Appl. Math. 60 (2000) 1-17. | Zbl 0962.49025

[12] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Acad. Press (1980). | MR 567696 | Zbl 0457.35001

[13] L. Lassoued and P. Mironescu, Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math. 77 (1999) 1-26. | Zbl 0930.35073

[14] N. Owen, J. Rubinstein and P. Sternberg, Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition. Proc. Roy. Soc. London Ser. A 429 (1990) 503-532. | Zbl 0722.49021

[15] J.F. Rodrigues, Obstacle Problems in Mathematical Physics. Mathematical Studies, North Holland (1987). | MR 880369 | Zbl 0606.73017

[16] S. Serfaty, Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part I. Comm. Contemporary Math. 1 (1999) 213-254. | Zbl 0944.49007

[17] S. Serfaty, Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part II. Comm. Contemporary Math. 1 (1999) 295-333. | Zbl 0964.49005

[18] S. Serfaty, Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation. Arch. Rational Mech. Anal. 149 (1999) 329-365. | Zbl 0959.35154

[19] S. Serfaty, Sur l'équation de Ginzburg-Landau avec champ magnétique, in Proc. of Journées Équations aux dérivées partielles, Saint-Jean-de-Monts (1998). | Numdam

[20] E. Sandier and S. Serfaty, Global Minimizers for the Ginzburg-Landau Functional below the First Critical Magnetic Field. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 119-145. | Numdam | Zbl 0947.49004

[21] E. Sandier and S. Serfaty, On the Energy of Type-II Superconductors in the Mixed Phase. Rev. Math. Phys. (to appear). | MR 1794239 | Zbl 0964.49006

[22] E. Sandier and S. Serfaty, A Rigorous Derivation of a Free-Boundary Problem Arising in Superconductivity. Annales Sci. École Norm. Sup. (4) 33 (2000) 561-592. | Numdam

[23] E. Sandier and S. Serfaty, Ginzburg-Landau Minimizers Near the First Critical Field Have Bounded Vorticity. Preprint. | MR 1979114 | Zbl 1037.49001

[24] D. Tilley and J. Tilley, Superfluidity and Superconductivity, 2nd edition. Adam Hilger Ltd., Bristol (1986).