PreprintCC BY 4.0arXiv
Infinite cascades for the defocusing cubic half-wave equation on the torus
Abstract
We construct global solutions of the defocusing cubic half-wave equation on the torus whose Hs norms grow exponentially for every 1/2<s<3/2. Such solutions exist at every positive mass. To the best of our knowledge, this provides the first example of a genuine infinite cascade for a defocusing fractional nonlinear Schrödinger equation on the torus. In particular, our result resolves an open question posed by Gérard and Grellier concerning the existence of unbounded Sobolev trajectories for the defocusing cubic half-wave equation on the torus.
Related
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- Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in Hs, s>1/2
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- Large-Data Global Well-Posedness for the Defocusing Cubic Schrödinger Equation in 3D Convex Domains
- Logarithmic concentration for the focusing cubic Schrödinger equation on the two-dimensional torus
BibTeX
@misc{chen2026infinite,
title = {{Infinite cascades for the defocusing cubic half-wave equation on the torus}},
author = {Xi Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.24930},
eprint = {2609.24930},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24930},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Infinite cascades for the defocusing cubic half-wave equation on the torus
AU - Xi Chen
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.24930
UR - https://arxiv.org/abs/2609.24930
AB - We construct global solutions of the defocusing cubic half-wave equation on the torus whose H^s norms grow exponentially for every 1/2<s<3/2. Such solutions exist at every positive mass. To the best of our knowledge, this provides the first example of a genuine infinite cascade for a defocusing fractional nonlinear Schrödinger equation on the torus. In particular, our result resolves an open question posed by Gérard and Grellier concerning the existence of unbounded Sobolev trajectories for the defocusing cubic half-wave equation on the torus.
ER -