Evolution of Polygonal Lines by the Binormal Flow
Copyright policy )Evolution of Polygonal Lines by the Binormal Flow
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.
minor changes
- University of Paris France
- Sorbonne Paris Cité France
- University of the Basque Country Spain
- Basque Center for Applied Mathematics Spain
- UNIVERSITE PARIS DESCARTES France
Compressible Navier-Stokes equations, nonlinear Schrödinger equations, binormal flow, Binormal flow, Curves in Euclidean and related spaces, NLS equations (nonlinear Schrödinger equations), Talbot effect, talbot effect, Nonlinear Schrödinger equations, PDEs in connection with fluid mechanics, Euler equations, Singular data, singular data, vortex filaments, 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)
Compressible Navier-Stokes equations, nonlinear Schrödinger equations, binormal flow, Binormal flow, Curves in Euclidean and related spaces, NLS equations (nonlinear Schrödinger equations), Talbot effect, talbot effect, Nonlinear Schrödinger equations, PDEs in connection with fluid mechanics, Euler equations, Singular data, singular data, vortex filaments, 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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