Standing Ring Blowup Solutions for Cubic NLS
Analysis of PDEs
2010-03-09 v2 Mathematical Physics
math.MP
Abstract
We prove there exist solutions to the focusing cubic nonlinear Schr\"odinger equation in three dimensions that blowup on a circle, in the sense of L^2 concentration on a ring, bounded H^1 norm outside any surrounding toroid, and growth of the global H^1 norm with the log-log rate. Analogous behaviour occurs in any higher dimension. That is, there exists data for which the corresponding evolution by cubic NLS explodes on a set of co-dimension two. To simplify the exposition, the proof is presented in dimension three, with remarks to indicate the adaptations in higher dimension.
Keywords
Cite
@article{arxiv.1002.1267,
title = {Standing Ring Blowup Solutions for Cubic NLS},
author = {Ian Zwiers},
journal= {arXiv preprint arXiv:1002.1267},
year = {2010}
}
Comments
54 pages. Introduction Updated