论文标题
立方非线性schr {Ö} dinger方程的全球适合性，初始位于$ l^{p} $ - 基于sobolev space
Global well-posedness for the cubic nonlinear Schr{ö}dinger equation with initial lying in $L^{p}$-based Sobolev spaces
论文作者
论文摘要
在本文中，我们继续我们的非线性Schrödinger方程（NLS）的研究[DSS20]，并具有无限的初始数据，这些数据在无穷大处不会消失。实际分析数据证明了$ \ Mathbb {R} $上的本地适应性。在这里，我们证明了1D NLS的全球适合度，只要初始数据足够光滑，任何$ 2 <p <\ infty $的初始数据都位于$ l^{p} $中。我们不使用立方非线性schr {Ö} dinger方程的完整集成性。
In this paper we continue our study [DSS20] of the nonlinear Schrödinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on $\mathbb{R}$ was proved for real analytic data. Here we prove global well-posedness for the 1D NLS with initial data lying in $L^{p}$ for any $2 < p < \infty$, provided the initial data is sufficiently smooth. We do not use the complete integrability of the cubic nonlinear Schr{ö}dinger equation.
