2维2次非线性薛定谔方程的整体有界性  

Global Boundedness for 2D Quadratic Nonlinear Schr?dinger Equation

作　　者：李俊峰 李想 LI Junfeng;LI Xiang(School of Mathematical Sciences,Dalian University of Technology,Dalian,Liaoning,116024,P.R.China;Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing,100875,P.R.China)

机构地区：[1]大连理工大学数学科学学院,大连辽宁116024 [2]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875

出　　处：《数学进展》2021年第4期496-510,共15页Advances in Mathematics（China）

基　　金：Supported by NSFC-DFG(No.11761131002)。

摘　　要：本文考虑2维2次的规范不变的非线性薛定谔方程,研究它在H^(0,2)(R^(2))上的整体有界性.并且通过导出波包中测试函数的渐近方程得到了它的修正散射.这种使用波包测试函数的方法容许同时考虑问题在物理空间和频率空间的渐近性质.In this paper,we consider the 2D quadratic gauge-invariant nonlinear Schrodinger equation.We set up its global bound in H^(0,2)(R^(2)).We also obtain its modified scattering by deriving an asymptotic equation for the test functions in the wave packets.This method allows us to consider the asymptotic properties of the problem both in the physical space and the frequency space.

关 键 词：整体有界性 临界指数 修正散射 2次非线性薛定谔方程 

分 类 号：O175.29[理学—数学]