On the existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space Mp,q (R)

被引：15

作者：

Chaichenets, Leonid ^{[1
]}

Hundertmark, Dirk ^{[1
]}

Kunstmann, Peer ^{[1
]}

Pattakos, Nikolaos ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Inst Anal, D-76128 Karlsruhe, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 08期

关键词：

NONLINEAR SCHRODINGER-EQUATION; DISPERSIVE EQUATIONS; WELL-POSEDNESS; WELLPOSEDNESS;

D O I：

10.1016/j.jde.2017.04.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove global existence for the one-dimensional cubic nonlinear Schrodinger equation in modulation spaces M-p,M-p' for p sufficiently close to 2. In contrast to known results, [9] and [14], our result requires no smallness condition on initial data. The proof adapts a splitting method inspired by work of Vargas-Vega, Hyakuna-Tsutsumi and Grunrock to the modulation space setting and exploits polynomial growth of the free Schrodinger group on modulation spaces. (C) 2017 Karlsruhe Institute of Technology. Published by Elsevier Inc. All tights reserved.

引用

页码：4429 / 4441

页数：13

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