We study solutions of the Gross-Pitaevsky equation and similar equations in space dimensions in a certain scaling limit, with initial data for which the jacobian concentrates around an (oriented) rectifiable dimensional set, say , of finite measure. It is widely conjectured that under these conditions, the jacobian at later times continues to concentrate around some codimension submanifold, say , and that the family of submanifolds evolves by binormal mean curvature flow. We prove this conjecture when is a round -dimensional sphere with multiplicity . We also prove a number of partial results for more general inital data.
@article{ASNSP_2002_5_1_4_733_0, author = {Jerrard, Robert L.}, title = {Vortex filament dynamics for {Gross-Pitaevsky} type equations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {733--768}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {4}, year = {2002}, mrnumber = {1991001}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2002_5_1_4_733_0/} }
TY - JOUR AU - Jerrard, Robert L. TI - Vortex filament dynamics for Gross-Pitaevsky type equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 733 EP - 768 VL - 1 IS - 4 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_2002_5_1_4_733_0/ LA - en ID - ASNSP_2002_5_1_4_733_0 ER -
%0 Journal Article %A Jerrard, Robert L. %T Vortex filament dynamics for Gross-Pitaevsky type equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 733-768 %V 1 %N 4 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_2002_5_1_4_733_0/ %G en %F ASNSP_2002_5_1_4_733_0
Jerrard, Robert L. Vortex filament dynamics for Gross-Pitaevsky type equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 4, pp. 733-768. http://archive.numdam.org/item/ASNSP_2002_5_1_4_733_0/
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