PreprintarXiv licencearXiv
Bilinear Strichartz estimates on the hyperbolic space and the cubic NLS
Abstract
We prove bilinear Strichartz estimates for the Schrödinger equation on the hyperbolic space. These bilinear estimates are then applied, as part of an I-method argument, to establish global well-posedness for the cubic defocusing nonlinear Schrödinger equation on the hyperbolic plane for regularities above 4/7. The I-method is implemented in physical space using a heat-based modified energy.
Related
- Bilinear Strichartz Estimates and Linear Morawetz Estimates for Schrödinger Operators with Potentials
- Sharp Shell-Type Bilinear Decoupling and Improved Strichartz Estimates on Tori
- Strichartz estimates for Klein-Gordon equations on asymptotically hyperbolic manifolds with applications
- Sharp critical Strichartz estimates for a resonant hyperbolic Schrödinger flow on the 3D waveguide
- Log-concavity and level set curvature estimates for the first Dirichlet eigenfunction in hyperbolic space
BibTeX
@misc{gavrus2026bilinear,
title = {{Bilinear Strichartz estimates on the hyperbolic space and the cubic NLS}},
author = {Cristian Gavrus},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32358},
eprint = {2610.32358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32358},
}
RIS
TY - UNPB
TI - Bilinear Strichartz estimates on the hyperbolic space and the cubic NLS
AU - Cristian Gavrus
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32358
UR - https://arxiv.org/abs/2610.32358
AB - We prove bilinear Strichartz estimates for the Schrödinger equation on the hyperbolic space. These bilinear estimates are then applied, as part of an I-method argument, to establish global well-posedness for the cubic defocusing nonlinear Schrödinger equation on the hyperbolic plane for regularities above 4/7. The I-method is implemented in physical space using a heat-based modified energy.
ER -