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.
Mots clés : vortices, Gross-Pitaevskii equations, superfluids
@article{COCV_2001__6__201_0,
author = {Serfaty, Sylvia},
title = {On a model of rotating superfluids},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {201--238},
publisher = {EDP-Sciences},
volume = {6},
year = {2001},
mrnumber = {1816073},
zbl = {0964.35142},
language = {en},
url = {http://www.numdam.org/item/COCV_2001__6__201_0/}
}
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] and, Topological Methods for the Ginzburg-Landau Equations. J. Math. Pures Appl. 77 (1998) 1-49. | Zbl
[2] (in preparation.)
[3] , and, Pinning Phenomena in the Ginzburg-Landau Model of Superconductivity. J. Math. Pures Appl. (to appear). | MR | Zbl
[4] and, Minimization of a Ginzburg-Landau type functional with nonvanishing Dirichlet boundary condition. Calc. Var. Partial Differential Equations (1998) 1-27. | Zbl
[5] , and, Ginzburg-Landau Vortices. Birkhäuser (1994). | MR | Zbl
[6] and, 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
[7] and, Remarks on sublinear elliptic equations. Nonlinear Anal. 10 (1986) 55-64. | Zbl
[8] and, Predicted signatures of rotating Bose-Einstein condensates. Nature 397 (1999) 327-329.
[9] and, Bose-Einstein condensates with vortices in rotating traps. Eur. Phys. J. D 7 (1999) 399-412.
[10] , 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] and, On a Discrete Variational Problem Involving Interacting Particles. SIAM J. Appl. Math. 60 (2000) 1-17. | Zbl
[12] and, An introduction to variational inequalities and their applications. Acad. Press (1980). | MR | Zbl
[13] and, Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math. 77 (1999) 1-26. | Zbl
[14] , and, 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
[15] , Obstacle Problems in Mathematical Physics. Mathematical Studies, North Holland (1987). | MR | Zbl
[16] , Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part I. Comm. Contemporary Math. 1 (1999) 213-254. | Zbl
[17] , Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part II. Comm. Contemporary Math. 1 (1999) 295-333. | Zbl
[18] , Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation. Arch. Rational Mech. Anal. 149 (1999) 329-365. | Zbl
[19] , Sur l'équation de Ginzburg-Landau avec champ magnétique, in Proc. of Journées Équations aux dérivées partielles, Saint-Jean-de-Monts (1998). | Numdam
[20] and, 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
[21] and, On the Energy of Type-II Superconductors in the Mixed Phase. Rev. Math. Phys. (to appear). | MR | Zbl
[22] and, A Rigorous Derivation of a Free-Boundary Problem Arising in Superconductivity. Annales Sci. École Norm. Sup. (4) 33 (2000) 561-592. | Numdam
[23] and, Ginzburg-Landau Minimizers Near the First Critical Field Have Bounded Vorticity. Preprint. | MR | Zbl
[24] and, Superfluidity and Superconductivity, 2nd edition. Adam Hilger Ltd., Bristol (1986).
