Strichartz estimates for Klein-Gordon equations on asymptotically hyperbolic manifolds with applications
Abstract
In this paper, we establish global-in-time Strichartz estimates for Klein-Gordon equations on non-trapping asymptotically hyperbolic manifolds. Our result is a positive-mass counterpart of the global Strichartz estimates of Sire, Sogge, Wang, and Zhang for shifted wave equations, and recovers the same range of admissible pairs. The main new feature is the low-frequency analysis, where the positive mass changes the spectral phase and leads to a different dispersive mechanism. Combining the resulting low-frequency estimates with microlocalized high-frequency estimates yields the full global Strichartz estimates. As applications, we obtain small-data global existence and scattering for power-type and certain derivative semilinear equations, as well as small-data global existence for a class of smooth semilinear equations without imposing a null condition.
Related
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- Inhomogeneous Strichartz estimates on manifolds with nonpositive curvature and applications
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BibTeX
@misc{dai2026strichartz,
title = {{Strichartz estimates for Klein-Gordon equations on asymptotically hyperbolic manifolds with applications}},
author = {Wei Dai and Chengbo Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11827},
eprint = {2610.11827},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11827},
}
RIS
TY - UNPB
TI - Strichartz estimates for Klein-Gordon equations on asymptotically hyperbolic manifolds with applications
AU - Wei Dai
AU - Chengbo Wang
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11827
UR - https://arxiv.org/abs/2610.11827
AB - In this paper, we establish global-in-time Strichartz estimates for Klein-Gordon equations on non-trapping asymptotically hyperbolic manifolds. Our result is a positive-mass counterpart of the global Strichartz estimates of Sire, Sogge, Wang, and Zhang for shifted wave equations, and recovers the same range of admissible pairs. The main new feature is the low-frequency analysis, where the positive mass changes the spectral phase and leads to a different dispersive mechanism. Combining the resulting low-frequency estimates with microlocalized high-frequency estimates yields the full global Strichartz estimates. As applications, we obtain small-data global existence and scattering for power-type and certain derivative semilinear equations, as well as small-data global existence for a class of smooth semilinear equations without imposing a null condition.
ER -