On the one dimensional cubic NLS in a critical space
Analysis of PDEs
2021-07-06 v1
Abstract
In this note we study the initial value problem in a critical space for the one dimensional Schr\"odinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by a sequence of Dirac deltas with different amplitudes but equispaced. This choice is motivated by a related geometrical problem; the one describing the flow of curves in three dimensions moving in the direction of the binormal with a velocity that is given by the curvature.
Cite
@article{arxiv.2107.01934,
title = {On the one dimensional cubic NLS in a critical space},
author = {Marco Bravin and Luis Vega},
journal= {arXiv preprint arXiv:2107.01934},
year = {2021}
}