欧氏空间上非线性Schrödinger方程Sobolev范数的增长OA
Growth of Sobolev Norms for Nonlinear Schrödinger Equation in Euclidean Space
通过构造修正能量泛函,研究二维欧氏空间中非线性Schrödinger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(sup t∈(0,T)||u||Hm≤Cmax{1,T}m-1+ϵ),所得结果完善了 NLS高阶正则性演化理论.
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.
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
数理科学
非线性Schrödinger方程Sobolev范数修正能量Strichartz估计
nonlinear Schrödinger equationSobolev normmodified energyStrichartz estimate
《吉林大学学报（理学版）》 2026 (3)
498-506,9
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:BK20230026BK20221497).
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