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#### Riemann's non-differentiable function and the binormal curvature flow

(2020-07-14)

We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ...

#### On the energy of critical solutions of the binormal flow

(2020-07-02)

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic ...

#### Evolution of Polygonal Lines by the Binormal Flow

(2020-06-01)

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 ...

#### Evolution of Polygonal Lines by the Binormal Flow

(2020-02-05)

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ...

#### On the energy of critical solutions of the binormal flow

(2019-07-20)

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ...

#### Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$

(2017-02-02)

In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ...

#### The initial value problem for the binormal flow with rough data

(2015-12-31)

In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ...