On a model of rotating superfluids
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 6, page 201-238
- ISSN: 1292-8119
Access Full Article
top
Abstract
topHow to cite
topSerfaty, Sylvia. "On a model of rotating superfluids." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 201-238. <http://eudml.org/doc/116573>.
@article{Serfaty2010,
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.
},
author = {Serfaty, Sylvia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Vortices; Gross-Pitaevskii equations; superfluids.; vortices; Gross-Pitaevskij equation; energy functional; rotating superfluids},
language = {eng},
month = {3},
pages = {201-238},
publisher = {EDP Sciences},
title = {On a model of rotating superfluids},
url = {http://eudml.org/doc/116573},
volume = {6},
year = {2010},
}
TY - JOUR
AU - Serfaty, Sylvia
TI - On a model of rotating superfluids
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 201
EP - 238
AB -
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.
LA - eng
KW - Vortices; Gross-Pitaevskii equations; superfluids.; vortices; Gross-Pitaevskij equation; energy functional; rotating superfluids
UR - http://eudml.org/doc/116573
ER -
References
top- L. Almeida and F. Bethuel, Topological Methods for the Ginzburg-Landau Equations. J. Math. Pures Appl.77 (1998) 1-49.
- 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).
- 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.
- H. Brezis and L. Oswald, Remarks on sublinear elliptic equations. Nonlinear Anal.10 (1986) 55-64.
- D.A. Butts and D.S. Rokhsar, Predicted signatures of rotating Bose-Einstein condensates. Nature397 (1999) 327-329.
- Y. Castin and R. Dum, Bose-Einstein condensates with vortices in rotating traps. Eur. Phys. J. D7 (1999) 399-412.
- 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 Astronomy30 (1976).
- S. Gueron and I. Shafrir, On a Discrete Variational Problem Involving Interacting Particles. SIAM J. Appl. Math.60 (2000) 1-17.
- D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Acad. Press (1980).
- L. Lassoued and P. Mironescu, Ginzburg-Landau type energy with discontinuous constraint. J. Anal. Math.77 (1999) 1-26.
- 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. A429 (1990) 503-532.
- J.F. Rodrigues, Obstacle Problems in Mathematical Physics. Mathematical Studies, North Holland (1987).
- S. Serfaty, Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part I. Comm. Contemporary Math.1 (1999) 213-254.
- S. Serfaty, Local Minimizers for the Ginzburg-Landau Energy near Critical Magnetic Field, Part II. Comm. Contemporary Math.1 (1999) 295-333.
- S. Serfaty, Stable Configurations in Superconductivity: Uniqueness, Multiplicity and Vortex-Nucleation. Arch. Rational Mech. Anal.149 (1999) 329-365.
- S. Serfaty, Sur l'équation de Ginzburg-Landau avec champ magnétique, in Proc. of Journées Équations aux dérivées partielles, Saint-Jean-de-Monts (1998).
- E. Sandier and S. Serfaty, Global Minimizers for the Ginzburg-Landau Functional below the First Critical Magnetic Field. Ann. Inst. H. Poincaré Anal. Non Linéaire17 (2000) 119-145.
- E. Sandier and S. Serfaty, On the Energy of Type-II Superconductors in the Mixed Phase. Rev. Math. Phys. (to appear).
- 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.
- 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).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.