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Sharp Strichartz estimates on quadratic irrational tori
Abstract
We prove sharp L4 Strichartz estimates for two-dimensional periodic Schrödinger flows with integral diagonal symbols ak12+bk22 where a,b ∈ ℤ ∖ {0}. The estimates exhibit a sharp arithmetic dichotomy according to whether −ab is a square: for frequencies bounded by N, the optimal loss is (log N)1/4 when −ab is not a square and N1/4 when −ab is a square. As a consequence, we show that arbitrarily small perturbations of the rectangular aspect ratio can lead to a transition between global well-posedness and norm inflation for cubic hyperbolic NLS.
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BibTeX
@misc{liang2026sharp,
title = {{Sharp Strichartz estimates on quadratic irrational tori}},
author = {Rui Liang and Shunlin Shen and Yuzhao Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21069},
eprint = {2609.21069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21069},
}
RIS
TY - UNPB
TI - Sharp Strichartz estimates on quadratic irrational tori
AU - Rui Liang
AU - Shunlin Shen
AU - Yuzhao Wang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21069
UR - https://arxiv.org/abs/2609.21069
AB - We prove sharp L^4 Strichartz estimates for two-dimensional periodic Schrödinger flows with integral diagonal symbols ak_1^2+bk_2^2 where a,b ∈ ℤ ∖ {0}. The estimates exhibit a sharp arithmetic dichotomy according to whether −ab is a square: for frequencies bounded by N, the optimal loss is (log N)^1/4 when −ab is not a square and N^1/4 when −ab is a square. As a consequence, we show that arbitrarily small perturbations of the rectangular aspect ratio can lead to a transition between global well-posedness and norm inflation for cubic hyperbolic NLS.
ER -