Long time dynamics for defocusing cubic NLS on three dimensional product space
Analysis of PDEs
2020-03-03 v1
Abstract
In this article, we study long time dynamics for defocusing cubic NLS on three dimensional product space. First, we apply the decoupling method in Bourgain-Demeter \cite{BD} to establish a bilinear Strichartz estimate. Moreover, we prove global well-posedness for defocusing, cubic NLS on three dimensional product space with rough initial data (, ) based on I-method and the bilinear estimate. At last, we discuss the growth of higher Sobolev norm problem which is tightly linked to the weak turbulence phenomenon.
Cite
@article{arxiv.2003.00665,
title = {Long time dynamics for defocusing cubic NLS on three dimensional product space},
author = {Zehua Zhao and Jiqiang Zheng},
journal= {arXiv preprint arXiv:2003.00665},
year = {2020}
}
Comments
15 pages