Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier Slow motion for gradient systems with equal depth multiple-well potentials. (English) Zbl 1213.35254 J. Differ. Equations 250, No. 1, 53-94 (2011). Reviewer: Jiaqi Mo (Wuhu) MSC: 35K57 35K15 PDFBibTeX XMLCite \textit{F. Bethuel} et al., J. Differ. Equations 250, No. 1, 53--94 (2011; Zbl 1213.35254) Full Text: DOI arXiv
Béthuel, Fabrice; Orlandi, Giandomenico; Smets, Didier On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation. (English) Zbl 1144.35399 Alama, Stanley (ed.) et al., Singularities in PDE and the calculus of variations. Selected papers of the CRM workshop, Montreal, Canada, July 17– 21, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4350-5/pbk). CRM Proceedings and Lecture Notes 44, 11-31 (2008). MSC: 35K55 35B40 35Q40 35K15 35B25 35A15 PDFBibTeX XMLCite \textit{F. Béthuel} et al., in: Singularities in PDE and the calculus of variations. Selected papers of the CRM workshop, Montreal, Canada, July 17-- 21, 2006. Providence, RI: American Mathematical Society (AMS). 11--31 (2008; Zbl 1144.35399)
Bethuel, F.; Orlandi, G.; Smets, D. Dynamics of multiple degree Ginzburg-Landau vortices. (English) Zbl 1135.35014 Commun. Math. Phys. 272, No. 1, 229-261 (2007). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35B25 58E50 35K55 PDFBibTeX XMLCite \textit{F. Bethuel} et al., Commun. Math. Phys. 272, No. 1, 229--261 (2007; Zbl 1135.35014) Full Text: DOI
Smets, Didier; Bethuel, Fabrice; Orlandi, Giandomenico Quantization and motion law for Ginzburg-Landau vortices. (English) Zbl 1105.76062 Arch. Ration. Mech. Anal. 183, No. 2, 315-370 (2007). MSC: 76Y05 35Q35 35Q40 PDFBibTeX XMLCite \textit{D. Smets} et al., Arch. Ration. Mech. Anal. 183, No. 2, 315--370 (2007; Zbl 1105.76062) Full Text: DOI
Bethuel, F.; Orlandi, G.; Smets, D. Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature. (English) Zbl 1103.35038 Ann. Math. (2) 163, No. 1, 37-163 (2006). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35K55 35Q35 53C44 35B25 35K15 49Q20 PDFBibTeX XMLCite \textit{F. Bethuel} et al., Ann. Math. (2) 163, No. 1, 37--163 (2006; Zbl 1103.35038) Full Text: DOI Euclid
Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier Dynamics of multiple degree Ginzburg-Landau vortices. (English) Zbl 1096.35014 C. R., Math., Acad. Sci. Paris 342, No. 11, 837-842 (2006). MSC: 35B40 35K55 35K15 PDFBibTeX XMLCite \textit{F. Bethuel} et al., C. R., Math., Acad. Sci. Paris 342, No. 11, 837--842 (2006; Zbl 1096.35014) Full Text: DOI
Bethuel, F.; Orlandi, Giandomenico; Smets, Didier Improved estimates for the Ginzburg-Landau equation: the elliptic case. (English) Zbl 1121.35052 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 4, No. 2, 319-355 (2005). Reviewer: Giuseppe Di Fazio (Catania) MSC: 35J60 35B35 35B45 35J20 46E35 47J30 58E50 PDFBibTeX XMLCite \textit{F. Bethuel} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 4, No. 2, 319--355 (2005; Zbl 1121.35052) Full Text: EuDML
Bethuel, F.; Orlandi, G.; Smets, D. Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics. (English) Zbl 1087.35008 Duke Math. J. 130, No. 3, 523-614 (2005). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35B25 35K55 35B05 PDFBibTeX XMLCite \textit{F. Bethuel} et al., Duke Math. J. 130, No. 3, 523--614 (2005; Zbl 1087.35008) Full Text: DOI
Bethuel, F.; Orlandi, G.; Smets, D. Approximations with vorticity bounds for the Ginzburg-Landau functional. (English) Zbl 1129.35329 Commun. Contemp. Math. 6, No. 5, 803-832 (2004). MSC: 35J20 35B25 46N20 47J30 PDFBibTeX XMLCite \textit{F. Bethuel} et al., Commun. Contemp. Math. 6, No. 5, 803--832 (2004; Zbl 1129.35329) Full Text: DOI
Bethuel, F.; Orlandi, G.; Smets, D. Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics. (French. English summary) Zbl 1067.35031 Proceedings of the conference on partial differential equations, Forges-les-Eaux, France, June 7–11, 2004. Exp. I–XIII. Paris: Centre National de la Recherche Scientifique, Groupement de Recherche 2434 (ISBN 2-7302-1221-3/pbk). Exp. No. X, 12 p. (2004). MSC: 35K55 35K15 35B25 58E50 82D55 PDFBibTeX XMLCite \textit{F. Bethuel} et al., in: Journées ``Équations aux dérivées partielles'', Forges-les-Eaux, France, 7 au 11 juin 2004. Exposés Nos. I--XIII. Paris: Centre National de la Recherche Scientifique, Groupement de Recherche 2434. Exp. No. X, 12 p. (2004; Zbl 1067.35031) Full Text: Numdam
Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier Motion of concentration sets in Ginzburg-Landau equations. (English) Zbl 1063.35075 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 13, No. 1, 3-43 (2004). Reviewer: Domingo Salazar (Coventry) MSC: 35K55 35B05 53C44 PDFBibTeX XMLCite \textit{F. Bethuel} et al., Ann. Fac. Sci. Toulouse, Math. (6) 13, No. 1, 3--43 (2004; Zbl 1063.35075) Full Text: DOI Numdam Numdam EuDML
Bethuel, F.; Orlandi, G.; Smets, D. Vortex rings for the Gross-Pitaevskii equation. (English) Zbl 1091.35085 J. Eur. Math. Soc. (JEMS) 6, No. 1, 17-94 (2004). MSC: 35Q56 58E50 82D55 35C07 PDFBibTeX XMLCite \textit{F. Bethuel} et al., J. Eur. Math. Soc. (JEMS) 6, No. 1, 17--94 (2004; Zbl 1091.35085) Full Text: DOI Link
Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier On an open problem for Jacobians raised by Bourgain, Brezis and mironescu. (English. Abridged French version) Zbl 1113.35315 C. R., Math., Acad. Sci. Paris 337, No. 6, 381-385 (2003). MSC: 35J20 35B25 49Q20 58E50 PDFBibTeX XMLCite \textit{F. Bethuel} et al., C. R., Math., Acad. Sci. Paris 337, No. 6, 381--385 (2003; Zbl 1113.35315) Full Text: DOI
Bethuel, Fabrice; Orlandi, Giandomenico; Smets, Didier Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature. (English. Abridged French version) Zbl 1031.35026 C. R., Math., Acad. Sci. Paris 336, No. 9, 719-723 (2003). MSC: 35B40 35K55 35K15 PDFBibTeX XMLCite \textit{F. Bethuel} et al., C. R., Math., Acad. Sci. Paris 336, No. 9, 719--723 (2003; Zbl 1031.35026) Full Text: DOI