发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Morningside Center of Mathematics; School of Mathematics and Statistics, Beijing Institute of Technology（中国科学院数学与系统科学研究院; 数学天元中心; 北京理工大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了三维离焦三次薛定谔方程在$H^s$（$s>\frac{1}{2}$）中的全局适定性与散射，通过结合$I$-方法和改进的长时间双线性估计，并利用方向相互作用恒等式与频率归纳得到关键估计。
AI 中文摘要
我们证明了三维离焦三次非线性薛定谔方程在$H^s(\mathbb{R}^3)$（$s>\frac{1}{2}$）中具有任意初始数据时的全局适定性与散射。证明结合了$I$-方法与改进的长时间双线性$L^2_{t,x}$估计，用于解的频率局部化分量。关键的high-low频率估计源自方向相互作用恒等式和对频率的归纳。
英文摘要
We prove global well-posedness and scattering for the three-dimensional defocusing cubic nonlinear Schrödinger equation with arbitrary initial data in H^s(R^3), $s>\frac{1}{2}$. The proof combines the $I$-method with improved long-time bilinear $L^2_{t,x}$ estimates for frequency-localized components of the solution. The key high--low frequency estimate follows from a directional interaction identity and an induction on frequency.
Comments32 pages. Comments are welcome!
