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Strichartz estimates on two-dimensional irrational tori
Abstract
We prove an L4 Strichartz estimate for the dispersion n12+αn22 on 𝕋2, for every α>0. The loss is controlled by the Shannon entropy of the normalized squared Fourier coefficients and the cardinality of their support S. In particular, we obtain a norm loss of (log#S)1/2 on fixed time intervals, with constants locally uniform in α. This provides an irrational-dispersion counterpart of the cardinality estimate of Herr and Kwak [Forum Math. Pi (2024)] and improves the Nε loss of Bourgain and Demeter [Ann. of Math. (2015)] to (log N)1/2 on frequency boxes. The proof combines weighted incidence estimates, smooth localization, and an entropy recursion.
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BibTeX
@misc{wang2026strichartz,
title = {{Strichartz estimates on two-dimensional irrational tori}},
author = {Ming Wang and Yuanjia Xiong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09689},
eprint = {2610.09689},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09689},
}
RIS
TY - UNPB
TI - Strichartz estimates on two-dimensional irrational tori
AU - Ming Wang
AU - Yuanjia Xiong
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09689
UR - https://arxiv.org/abs/2610.09689
AB - We prove an L^4 Strichartz estimate for the dispersion n_1^2+αn_2^2 on 𝕋^2, for every α>0. The loss is controlled by the Shannon entropy of the normalized squared Fourier coefficients and the cardinality of their support S. In particular, we obtain a norm loss of (log#S)^1/2 on fixed time intervals, with constants locally uniform in α. This provides an irrational-dispersion counterpart of the cardinality estimate of Herr and Kwak [Forum Math. Pi (2024)] and improves the N^ε loss of Bourgain and Demeter [Ann. of Math. (2015)] to (log N)^1/2 on frequency boxes. The proof combines weighted incidence estimates, smooth localization, and an entropy recursion.
ER -