Search
Now showing items 1-5 of 5
Riemann's non-differentiable function and the binormal curvature flow
Banica, V.; Vega, L.
(2020-07-14)
(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 ...
Evolution of Polygonal Lines by the Binormal Flow
Banica, V.; Vega, L. (2020-02-05)
(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
Banica, V.; Vega, L. (2019-07-20)
(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 $\mathbb{S}^2$
Banica, V.; Vega, L. (2017-02-02)
(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
Banica, V.; Vega, L. (2015-12-31)
(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 ...