Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations

Communications in Mathematical Physics

Volumn 180, Issue 2, 1996, Pages 389-428

  Weinstein, M I ^a   Xin, J ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030500197     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02099719     Document Type: Article

References (38)

1. Aronson, D.G.: Bounds for fundamental solutions of a parabolic equation. Bull. Am. Math. Soc. 73, 890-896 (1967)
2. Aronson, D.G., Serrin, J.: Local behavior of solutions of quasilinear parabolic equations. Arch. Rational Mech. Anal. 25, 81-122 (1967)
3. Bauman, P., Chen, C., Phillips, D., Sternberg, P.: Vortex Annihilation in Nonlinear Heat Flow for Ginzburg-Landau Systems. European J. Appl. Math, to appear, 1995
4. Bethuel, T., Brezis, H., Helein, F.: Ginzburg-Landau Vortices. Boston: Birkhauser, 1994
5. Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger Operators. Berlin-Heidelber-New York: Springer-Verlag Texts and Monographs in Physics, 1987
6. Berestycki, H., Nirenberg, L.: On the Method of Moving Planes and the Sliding Method. Bol. da Soc. Brasileria da Matematica 22, 1-37 (1991)
7. Creswick, R., Morrison, H.: Phys. Lett. A 76, 267 (1980)
8. Davies, E.B.: Heat Kernels and Spectral Theory. Cambridge: Cambridge Univ. Press, 1989
9. Demoulini, S., Stuart, D.: Gradient Flow of the Superconducting Ginzburg-Landau Functional on the Plane. Preprint, 1995
10. Donnelly, R.J.: Quantized Vortices in Helium II. Cambridge: Cambridge Univ. Press, 1991
11. E, W.: Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Physica D 77, 383-404 (1994)
12. Ercolani, N., Montgomery, R.: On the fluid approximation to a nonlinear Schrödinger equation. Phys. Lett. A 180, 402-408 (1993)
13. Fabes, E.B., Stroock, W.B.: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash. Arch. Rational Mech. Anal. 96, 327-338 (1986)
14. 2. Quart. Appl. Math, to appear
15. Frisch, T., Pomeau, Y., Rica, S.: Transition to Dissipation in a Model of Superflow. Phys. Rev. Lett. 69, No. 11, 1644-1647 (1992)
16. Jaffe, A., Taubes, C.: Vortices and Monopoles. Boston: Birkhäuser, 1980
17. Jensen, A., Kato, T.: Spectral properties of Schrödinger operators and time decay of wave functions. Duke Math. J. 46, 583-611 (1979)
18. Levermore, C.D., Xin, J.: Multidimensional Stability of Traveling Waves in a Bistable Reaction-Diffusion Equation, Part II. Comm. PDE 17(11 & 12), 1901-1924 (1992)
19. Lieb, E.H., Loss, M.: Symmetry of the Ginzburg-Landau minimizer in a disc. Math. Res. Lett, 1, No. 8, 701-715 (1994)
20. Lin, F.-H.: Some Dynamical Properties of Ginzburg-Landau Vortices. Comm. Pure Appl. Math, to appear
21. Lin, F.-H.: A Remark on the Previous Paper "Some Dynamical Properties of Ginzburg-Landau Vortices". Preprint 1995
22. Mironescu, P.: On the Stability of Radial Solutions of the Ginzburg-Landau Equation. J. Func. Anal. 130, 334-344 (1995)
23. Nash, J.: Continuity of solutions of parabolic and elliptic equations. Am. J. Math. 80, 931-954 (1958)
24. Neu, J.: Vortices in the Complex Scalar Fields. Physica D 43, 385-406 (1990)
25. Newell, A.C.: Envelope equations. In: Nonlinear Wave Motion, Providence. RI: AMS, 1974, pp. 157-163
26. Norris, J.R.: Long time behavior of heat flow: Global estimates and exact asymptotics. 1995, preprint
27. Osada, H.: Diffusion processes with generators of generalized divergence form. J. Math. Kyoto Univ. (27-4), 597-619 (1987)
28. Pazy, A.: Semigroups of Linear Operators and Applications to PDE. Berlin-Heidelberg-New York: Springer Applied Math Sci. 44, 1983
29. Pego, R.L., Weinstein, M.I.: Eigenvalues, and solitary wave instabilities. Phil. Trans. R. Soc. Lond. A 340, 47-92 (1992)
30. Pismen, L., Rubinstein, J.: Dynamics of defects. In Nematics: Mathematical and Physical Aspects. J.M. Coron et. al. eds., Amsderdam: Kluwer Pubs, 1990
31. Rubinstein, J., Sternberg, P.: On the slow motion of vortices in the Ginzburg-Landau heat flow. SIAM J Math Anal, to appear
32. Simon, B.: Functional Integration and Quantum Physics. New York: Academic Press, 1979
33. Soffer, A., Weinstein, M.: Multichannel Scattering for Nonintegrable Equations, II, The Case of Anisotropic Potentials and Data. J. Diff. Eqs. 98, No. 2, 376-390 (1992)
34. Weinstein, W.: On the Vortex Solutions of Some Nonlinear Scalar Field Equations. Rocky Mountain J. Math, 21, No. 2, Spring, 821-826 (1991)
35. Weissler, F.: Existence and Non-existence of Global Solutions for a Semilinear Heat Equation. Isl J. Math. 38, No. 2, 1-2, 29-40 (1981)
36. Xin, J.: Multidimensional Stability of Traveling Waves in a Bistable Reaction-Diffusion Equation. Part I. Comm. PDE 17(11 & 12), 1889-1899 (1992)
37. Xin, J.: Existence of Planar Flame Fronts in Convective-Diffusive Periodic Media. Arch. Rat. Mech. Anal. 121, 205-233 (1992)
38. Xin, J.: Existence of a Class of Symmetric Rotating Spiral Waves on Finite Disc Domains in Excitable Media. Indiana Univ. Math. J. 42, No. 4, Winter 1305-1337 (1993)