On the NLS dynamics for infinite energy vortex configurations on the plane

Revista Matematica Iberoamericana

Volumn 24, Issue 2, 2008, Pages 671-702

  Bethuel, Fabrice ^a   Jerrard, Robert L ^b   Smets, Didier ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Nls equation; Superfluids; Vortex dynamics

Indexed keywords

EID: 54049089582     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/552     Document Type: Article

References (14)

1. ALMEIDA, L.: Threshold transition energies for Ginzburg-Landau functioals. Nonlinearity 12 (1999), 1389-1414.
2. GOLOVATY, D. AND BERLYAND, L.: On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains. Calc. Var. Partial Differential Equations 14 (2002), 213-232.
3. BETHUEL, F., BREZIS, H. AND HÉLEIN, F.: Ginzburg-Landau vortices. Progress in Nonlinear Differential Equations and their Applications 13. Birkhäuser, Boston, MA, 1994.
4. BETHUEL, F., BREZIS, H. AND ORLANDI, G.: Small energy solutions to the Ginzburg-Landau equation. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000), 763-770.
5. BETHUEL, F., ORLANDI, G. AND SMETS, D.: Dynamics of multiple degree Ginzburg-Landau vortices. Comm. Math. Phys. 272 (2007), 229-261.
6. BETHUEL, F. AND SMETS, D.: A remark on the Cauchy problem for the 2D Gross-Pitaevskii equation with non zero degree at infinity. Differential Integral Equations 20 (2007), 325-338.
7. CHIRON, D.: Boundary problems for the Ginzburg-Landau equation. Commun. Contemp. Math. 7 (2005), 597-648.
8. COLLIANDER, J. E. AND JERRARD, R. L.: Vortex dynamics for the Ginzburg-Landau-Schrodinger equation. Internat. Math. Res. Notices 1998, no. 7, 333-358.
9. JERRARD, R. L. AND SONER, H. M.: The Jacobian and the Ginzburg- Landau energy. Calc. Var. Partial Differential Equations 14 (2002), 151-191.
10. JERRARD, R. L. AND SPIRN, D.: Refined Jacobian estimates for Ginzburg-Landau functionals. Indiana Univ. Math. J. 56 (2007), 135-186.
11. JERRARD, R. L. AND SPIRN, D.: Refined Jacobian estimates and Gross-Pitaevsky vortex dynamics. Arch. Rat. Mech. Anal., to appear.
12. 2. Potential Anal. 5 (1996), 591-609.
13. LIN, F.-H. AND XIN, J. X.: On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation. Comm. Math. Phys. 200 (1999), 249-274.
14. MIRONESCU, P.: Les minimiseurs locaux pour l'équation de Ginzburg-Landau sont à symétrie radiale. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 593-598.