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Article Dans Une Revue Annals of PDE Année : 2020

Evolution of polygonal lines by the binormal flow

Résumé

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger 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 Schrödinger equation.
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Dates et versions

hal-01842121 , version 1 (17-07-2018)

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Valeria Banica, Luis Vega. Evolution of polygonal lines by the binormal flow. Annals of PDE, 2020, 6, Paper No.6, 53pp. ⟨hal-01842121⟩
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