Ginzburg-Landau vortices: Weak stability and schrödinger equation dynamics

Journal d'Analyse Mathematique

Volumn 77, Issue , 1999, Pages 129-205

  Colliander, J E ^a   Jerrard, R L ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033475315     PISSN: 00217670     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02791260     Document Type: Article

References (24)

1. G. Albert, R. L. Jerrard, and H. M. Soner, Functions of bounded n-variation, in preparation.
2. F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994.
3. F. Bethuel and X. Zheng, Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal. 80 (1988), 60-75.
4. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I,II, Geom. Funct. Anal. 3 (1993), 107-156, 209-262.
5. H. Brézis, J. M. Coron and E. Lieb, Harmonic maps with defects, Comm. Math. Phys. 107 (1986), 649-705.
6. H. Brezis and L. Nirenberg, Degree theory and BMO: Part i: compact manifolds without boundaries, Selecta Math. (N.S.) 1 (1995), 197-263.
7. J. E. Colliander and R. L. Jerrard, Vortex dynamics for the Ginzburg-Landau-Schrödinger equation, Internat. Math. Res. Notices (1998), 333-358.
8. B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989.
9. L. C. Evans and W. Gangbo, Differential equation methods for the Monge-Kantorovitch mass transfer problem, to appear.
10. V. L. Ginzburg and L. P. Pitaevskii, On the theory of superfluidity, Soviet Physics JETP 34 (7)(5) (1958), 858-861.
11. E. P. Gross, Dynamics of interacting bosons, in Physics of Many Particle Systems (E. Meeron, ed.), Gordon and Breech, New York, 1966, pp. 231-406.
12. R. L. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals, SIAM Math. Anal., to appear.
13. R. L. Jerrard, Vortex dynamics for the Ginzburg-Landau wave equation, Calc. Var. Partial Differential Equations, to appear.
14. R. L. Jerrard and H. M. Soner, Dynamics of Ginzburg-Landau vortices, Arch. Rational Mech. Anal. 142 (1998), 99-125.
15. F-H. Lin, Vortex dynamics for the nonlinear wave equations, preprint, 1997.
16. F. H. Lin, Solutions of Ginzburg-Landau equations and critical points of the renormalized energy, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 599-622.
17. F. H. Lin, Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure. Appl. Math. 49 (1996), 323-359.
18. F. H. Lin, A remark on the previous paper: "Some dynamical properties of Ginzburg-Landau vortices", Comm. Pure. Appl. Math, 49 (1996), 361-364.
19. C. Marchioro and M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids, Springer, Berlin, 1994.
20. S. Müller, Det = det. A remark on the distributional determinant, Comptes Rendus Acad. Sci. Paris 311 (1) (1990), 13-17.
21. L. P. Pitaevskii, Vortex lines in an imperfect Base gas, Soviet Physics JETP 13 (2) (1961), 451-454.
22. E. Sandier, Lower bounds for the energy of unit vector fields and applications, preprint, 1997.
23. M. Struwe, On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions, Differential Integral Equations 7 (1994), 1613-1624.
24. D. R. Tilley and J. Tilley, Superfluidity and Superconductivity, Adam Hilger Ltd., Bristol and Boston, 1986.