Year: 2013
Type: preprint
Abstract: The spatially periodic initial problem and Cauchy problem for nonlinear Schrödinger equations are considered. The existence and uniqueness of global solution with infinite smooth initial data $u_0$, i.e. $u_0,\;|u_0|^{2p}u_0\in H^{\infty}$, are established. Moreover these two problem with initial data $u_0\in H^m$ are globally well-posed provided the Fourier frequency of $u_0$ is contained in a bounded compact set. The equations studied here cover $L^2$ and $\dot{H}^1$ critical and supercritical, defocusing and focusing nonlinear Schr$\ddot{o}$dinger equations.
Source: arXiv (Cornell University)
Author: Han, Yongqian
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394643555