吉林大学学报（理学版）2026，Vol.64Issue(3)：498-506,9.DOI:10.13413/j.cnki.jdxblxb.2025258
欧氏空间上非线性Schrödinger方程Sobolev范数的增长
Growth of Sobolev Norms for Nonlinear Schrödinger Equation in Euclidean Space
摘要
Abstract
By constructing a modified energy functional,we investigated the temporal growth of higher-order Sobolev norms for the nonlinear Schrödinger equation(NLS)in two-dimensional Euclidean spaces.Based on results for cubic nonlinearities,we established a polynomial bound applicable to arbitrary higher-order nonlinearities(supt∈(0,T)||u||Hm ≤Cmax{ 1,T}m-1+ϵ).The obtained results improved the theory of higher-order regularity evolution for NLS.关键词
非线性Schrödinger方程/Sobolev范数/修正能量/Strichartz估计Key words
nonlinear Schrödinger equation/Sobolev norm/modified energy/Strichartz estimate分类
数理科学引用本文复制引用
陈怡,张晓岭..欧氏空间上非线性Schrödinger方程Sobolev范数的增长[J].吉林大学学报（理学版）,2026,64(3):498-506,9.基金项目
国家自然科学基金(批准号:U2340221)和江苏省自然科学基金(批准号:BK20230026 （批准号:U2340221）
BK20221497). （）
