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.

We study solutions of the Gross-Pitaevsky equation and similar equations in m3 space dimensions in a certain scaling limit, with initial data u 0 ϵ for which the jacobian Ju 0 ϵ concentrates around an (oriented) rectifiable m-2 dimensional set, say Γ 0 , of finite measure. It is widely conjectured that under these conditions, the jacobian at later times t>0 continues to concentrate around some codimension 2 submanifold, say Γ t , and that the family {Γ t } of submanifolds evolves by binormal mean curvature flow. We prove this conjecture when Γ 0 is a round m-2-dimensional sphere with multiplicity 1. We also prove a number of partial results for more general inital data.

Classification: 35B25, 35Q55
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     title = {Vortex filament dynamics for {Gross-Pitaevsky} type equations},
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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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