Refined Jacobian estimates and Gross-Pitaevsky vortex dynamics

Archive for Rational Mechanics and Analysis

Volumn 190, Issue 3, 2008, Pages 425-475

  Jerrard, Robert Leon ^a   Spirn, Daniel ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54349128348     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0167-8     Document Type: Article

References (36)

1. G. Alberti C. Baldo G. Orlandi 2003 Functions with prescribed singularities J. Eur. Math. Soc. 5 275 311
2. N.D. Alikakos L. Bronsard G. Fusco 1998 Slow motion in the gradient theory of phase transitions via energy and spectrum Calc. Var. Partial Differ. Equ. 6 39 66
3. N. Alikakos G. Fusco 1998 Slow dynamics for the Cahn-Hilliard equation in higher space dimensions: the motion of bubbles Arch. Rational Mech. Anal. 141 1 61
4. Bethuel, F., Brezis, H., Helein, F.: Ginzburg-Landau Vortices. Progress in Nonlinear Differential Equations and their Applications, 13. Birkhäuser, Boston, 1994
5. F. Bethuel G. Orlandi D. Smets 2005 Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics Duke Math. J. 130 523 614
6. H. Brezis J.-M. Coron E. Lieb 1986 Harmonic maps with defects Comm. Math. Phys. 107 649 705
7. V.S. Buslaev G.S. Perelman 2003 Scattering for the nonlinear Schrödinger equation: states close to a soliton St. Petersburg Math. J. 4 1111 1142
8. V.S. Buslaev C. Sulem 2003 On asymptotic stability of solitary waves for nonlinear Schrödinger equations Ann. Inst. H. Poincaré Anal. Non Linéaire 20 419 475
9. J.E. Colliander R.L. Jerrard 1998 Vortex dynamics for the Ginzburg-Landau-Schrödinger equation Internat. Math. Res. Notices 1998 333 358
10. J.E. Colliander R.L. Jerrard 1999 Ginzburg-Landau vortices: weak stability and Schrödinger equation dynamics J. Anal. Math. 77 129 205
11. P. de Mottoni M. Schatzman 1995 Geometrical evolution of developed interfaces Trans. Am. Math. Soc. 347 1533 1589
12. M. del Pino P. Felmer M. Kowalczyk 2004 Minimality and nondegeneracy of degree-one Ginzburg-Landau vortex as a Hardy's type inequality Int. Math. Res. Not. 2004 1511 1527
13. E W.: Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Phys. D 77, 383-404 (1994)
14. A.L. Fetter 1966 Vortices in an imperfect Bose Gas. IV. Translational Velocity Phys. Rev. 151 100 104
15. S. Gustafson I.M. Sigal 2000 The stability of magnetic vortices Comm. Math. Phys. 212 257 275
16. S. Gustafson I.M. Sigal 2006 Effective dynamics of magnetic vortices Adv. Math. 199 448 498
17. R.L. Jerrard 1999 Vortex dynamics for the Ginzburg-Landau wave equation Calc. Var. Partial Differ. Equ. 9 683 688
18. R.L. Jerrard H.M. Soner 2002 The Jacobian and the Ginzburg-Landau energy Calc. Var. Partial Differ. Equ. 14 151 191
19. R.L. Jerrard H.M. Soner 1998 Dynamics of Ginzburg-Landau vortices Arch. Rational Mech. Anal. 142 99 125
20. R.L. Jerrard D. Spirn 2007 Refined Jacobian estimates for Ginzburg-Landau functionals Indiana Univ. Math. J. 56 135 186
21. V.I. Klyatskin 1966 Sound radiation by a system of vortices Izv. AN SSSR Mekhanika Zhidkosti i Gza 1 87 92
22. F.-H. Lin 1996 Some dynamical properties of Ginzburg-Landau vortices Comm. Pure Appl. Math. 49 323 359
23. F.-H. Lin 1999 Vortex dynamics for the nonlinear wave equation Comm. Pure Appl. Math. 52 737 761
24. F.-H. Lin J. Xin 1999 On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation Comm. Math. Phys. 200 249 274
25. Marchioro, C., Pulvirenti, M.: Mathematical Theory of Incompressible Nonviscous Fluids. Appl. Math. Sci., 96. Springer, New York, 1994
26. Y. Martel F. Merle T.-P. Tsai 2002 Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations Comm. Math. Phys. 231 347 373
27. J. Neu 1990 Vortices in the complex scalar fields Phys. D 43 385 406
28. Yu.N. Ovchinnikov I.M. Sigal 1998 Long-time behaviour of Ginzburg-Landau vortices Nonlinearity 11 1295 1309
29. Roitberg, Y.: Elliptic Boundary Value Problems in the Space of Distributions. Mathematics and its Applications, vol. 498. Kluwer, Dordrecht, 1999
30. E. Sandier S. Serfaty 2004 Gamma-convergence of gradient flows with applications to Ginzburg-Landau Comm. Pure Appl. Math. 57 1627 1672
31. Sandier, E., Serfaty, S.: Vortices in the magnetic Ginzburg-Landau model. Progress in Nonlinear Differential Equations and their Applications, vol. 70. Birkhäuser, Boston, 2007
32. 2 C. R. Acad. Sci. Paris S^r. I Math. 318 327 331
33. A. Soffer M.I. Weinstein 1990 Multichannel nonlinear scattering for non-integrable equations Comm. Math. Phys. 133 119 146
34. D. Spirn 2003 Vortex motion law for the Schrödinger-Ginzburg-Landau equations SIAM J. Math. Anal. 34 1435 1476
35. D. Stuart 1994 Dynamics of Abelian Higgs vortices in the near Bogomolny regime Comm. Math. Phys. 159 51 91
36. T.-P. Tsai H.-T. Yau 2002 Relaxation of excited states in nonlinear Schrödinger equations Int. Math. Res. Notices 2002 1629 1673