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Evolution of Polygonal Lines by the Binormal Flow

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 25 May 2020Embargo end date: 01 Jan 2018 France, Spain Publisher:Springer Science and Business Media LLCJournal:Annals of PDE, volume 6 (issn: 2524-5317, eissn: 2199-2576,

Authors: Banica, Valeria; Vega, Luis;

doi: 10.1007/s40818-020-0078-z , 10.48550/arxiv.1807.06948

arXiv: http://arxiv.org/abs/1807.06948

handle: 20.500.11824/1087 , 20.500.11824/1345

Evolution of Polygonal Lines by the Binormal Flow

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Abstract

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr{��}dinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally we prove the existence of a unique solution of the binormal flow with datum a polygonal line. This equation is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. We also construct solutions of the binormal flow that present an intermittency phenomena. Finally, the solution we construct for the binormal flow is continued for negative times, yielding a geometric way to approach the continuation after blow-up for the 1-D cubic nonlinear Schr{��}dinger equation.

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Countries

France, Spain

Related Organizations

French National Centre for Scientific Research
France
Sorbonne University
France
Laboratoire d'informatique de Paris 6
France
Ministry of Higher Education and Research
France
University of Paris
France

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Keywords

nonlinear Schrödinger equations, Binormal flow, Talbot effect, talbot effect, Nonlinear Schrödinger equations, Singular data, Binormal Flow, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Vortex filaments, Analysis of PDEs (math.AP)

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	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%