Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori
Analysis of PDEs
2022-08-02 v3 Classical Analysis and ODEs
Number Theory
Abstract
We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.
Cite
@article{arxiv.1810.05630,
title = {Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori},
author = {Yu Deng and Pierre Germain and Larry Guth and Simon Myerson},
journal= {arXiv preprint arXiv:1810.05630},
year = {2022}
}
Comments
28 pages