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arXiv · 1307.1304

Global Smooth Solution of Nonlinear Schr\"odinger Equation

Yongqian Han
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Abstract

The spatially periodic initial problem and Cauchy problem for nonlinear Schr\"odinger 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.

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Yongqian Han. 2013-07-04. Global Smooth Solution of Nonlinear Schr\"odinger Equation. https://arxiv.org/abs/1307.1304

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