Lin, Fang Hua Solutions of Ginzburg-Landau equations and critical points of the renormalized energy. (English) Zbl 0845.35052 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 12, No. 5, 599-622 (1995). The motion of vortices of solutions of the initial boundary value problem of the Ginzburg-Landau equation is the main concern of this paper, and the question is studied successfully. There are connections to the complete characterization of asymptotic behavior for vortices (governed by a certain energy functional), given in the book of F. Bethuel, H. Brezis and F. Hélein [Ginzburg-Landau vortices, Birkhäuser, Boston (1994; Zbl 0802.35142)]. Reviewer: A.Göpfert (Halle) Cited in 31 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:motion of vortices; Ginzburg-Landau equation Citations:Zbl 0802.35142 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] Bethuel, F.; Brezis, H.; Helein, F., Ginzburg-Landau vertices (1994), Birkhaüser: Birkhaüser Boston · Zbl 0802.35142 [2] Bethuel, F.; Brezis, H.; Helein, F., Asymptotics for the minimization of a Ginzburg-Landau functional, Cal. variations and P.D.E., Vol. 1#2, 123-148 (1993) · Zbl 0834.35014 [4] Chen, Y. M.; Lin, F. H., Evaluation of harmonic maps with the Dirichlet boundary condition, Comm. in Analysis and Geometry, Vol. 1#3, 327-346 (1993) · Zbl 0845.35049 [5] Chen, Y. M.; Struwe, M., Existence and partial regularity for heat flow for harmonic maps, Math. Z, Vol. 201, 83-103 (1989) · Zbl 0652.58024 [9] Neu, J., Vortex dynamics of complex scalar fields, Physics D, Vol. 43, 384-406 (1990) · Zbl 0711.35024 [10] Pismen, L.; Rubinstein, J., (Coron, J. M.; etal., Dynamics of defects, in nematics, mathematical and physical aspects (1991), Kluwer Pubs) · Zbl 0850.76045 [13] Simon, L., Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Annals of Math, Vol. 118, 527-571 (1983) · Zbl 0549.35071 [14] Struwe, M., On the asymptotic behavior of minimizers of the Ginsburg-Landau model in 2 dimensions, J. Diff. Int. Eqs, Vol. 7 (1994) [15] Struwe, M., On the evolution of harmonic maps of Riemannian surfaces, Comment. Math. Helv., Vol. 60, 558-581 (1985) · Zbl 0595.58013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.