发表机构
South China Normal University; University of Science and Technology of China; University of Birmingham（华南师范大学; 中国科学技术大学; 伯明翰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明二维周期薛定谔流在积分对角符号下的尖锐L^4 Strichartz估计，揭示算术二分性，并应用于三次双曲NLS的适定性转变。
AI 中文摘要
我们证明了二维周期薛定谔流在积分对角符号 $ak_{1}^2+bk_2^2$（其中 $a,b \in \mathbb Z \setminus \{0\}$）下的尖锐 $L^{4}$ Strichartz估计。这些估计根据 $-ab$ 是否为平方数展现出尖锐的算术二分性：对于频率以 $N$ 为界的情况，当 $-ab$ 不是平方数时最优损失为 $(\log N)^{1/4}$，当 $-ab$ 是平方数时最优损失为 $N^{1/4}$。作为推论，我们证明矩形纵横比的任意小扰动可导致三次双曲NLS的全局适定性与范数膨胀之间的转变。
英文摘要
We prove sharp $L^{4}$ Strichartz estimates for two-dimensional periodic Schrödinger flows with integral diagonal symbols $ak_{1}^2+bk_2^2$ where $a,b \in \mathbb Z \setminus \{0\}$. 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.
