欧氏空间上非线性Schrodinger方程Sobolev范数的增长

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (3): 498-0506.

欧氏空间上非线性Schrodinger方程Sobolev范数的增长

陈怡, 张晓岭

河海大学数学学院, 江苏省高校重点实验室“水系统数学建模与智能计算”, 南京 210098

收稿日期:2025-09-10 出版日期:2026-05-26 发布日期:2026-05-26
通讯作者: 张晓岭 E-mail:xlzhang@hhu.edu.cn

Growth of Sobolev Norms for Nonlinear Schrodinger Equation in Euclidean Space

CHEN Yi, ZHANG Xiaoling

Laboratory of Mathematical Modeling and Intelligent Computing for Water Systems, School of Mathematics, Hohai University, Nanjing 210098, China

Received:2025-09-10 Online:2026-05-26 Published:2026-05-26

摘要/Abstract

摘要： 通过构造修正能量泛函, 研究二维欧氏空间中非线性Schrodinger方程（NLS）高阶 Sobolev 范数的时间增长性. 基于三次非线性项结果, 建立了任意高阶非线性项的多项式界，所得结果完善了NLS高阶正则性演化理论.

关键词: 非线性Schrodinger方程, Sobolev范数, 修正能量, Strichartz估计

Abstract: By constructing a modified energy functional, we investigated the temporal growth of higher-order Sobolev norms for the nonlinear Schrodinger equation (NLS) in two-dimensional Euclidean spaces. Based on results for cubic nonlinearities, we established a polynomial bound applicable to arbitrary higher-order nonlinearities. The obtained results improved the theory of higher-order regularity evolution for NLS.

Key words: nonlinear Schrodinger equation, Sobolev norm, modified energy, Strichartz estimate

中图分类号:

O175.29

陈怡, 张晓岭. 欧氏空间上非线性Schrodinger方程Sobolev范数的增长[J]. 吉林大学学报(理学版), 2026, 64(3): 498-0506.

CHEN Yi, ZHANG Xiaoling. Growth of Sobolev Norms for Nonlinear Schrodinger Equation in Euclidean Space[J]. Journal of Jilin University Science Edition, 2026, 64(3): 498-0506.