Strichartz estimates and global well-posedness of the cubic NLS on

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2024-09-09 DOI:10.1017/fmp.2024.11

Sebastian Herr, Beomjong Kwak

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引用次数: 0

Abstract

The optimal

$L^4$

-Strichartz estimate for the Schrödinger equation on the two-dimensional rational torus

$\mathbb {T}^2$

is proved, which improves an estimate of Bourgain. A new method based on incidence geometry is used. The approach yields a stronger

$L^4$

bound on a logarithmic time scale, which implies global existence of solutions to the cubic (mass-critical) nonlinear Schrödinger equation in

$H^s(\mathbb {T}^2)$

for any

$s>0$

and data that are small in the critical norm.

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立方 NLS 的斯特里查兹估计值和全局良好性

证明了二维有理环 $\mathbb {T}^2$ 上薛定谔方程的最优 $L^4$ -Strichartz 估计值，它改进了布尔甘的估计值。使用了一种基于入射几何的新方法。该方法在对数时间尺度上得到了更强的 $L^4$ 约束，这意味着对于任意 $s>0$ 和在临界规范中很小的数据，在 $H^s(\mathbb {T}^2)$ 中的三次（质量临界）非线性薛定谔方程的解全局存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

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