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Bull. Korean Math. Soc. 2011; 48(6): 1291-1302

Printed November 1, 2011

https://doi.org/10.4134/BKMS.2011.48.6.1291

Copyright © The Korean Mathematical Society.

Local well-posedness for the nonlinear Schr\"odinger equation with harmonic potentila in $H^s$

Shan Zhang, Zuhan Liu, and Zhongxue L\"u

Yangzhou University, Xuzhou Normal University, Xuzhou Normal University

Abstract

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We establish the local well-posedness for the Cauchy problem of the nonlinear Schr\"{o}dinger equation with harmonic potential in $H^{s}(\mathbb{R}^{n})$, where $s\in \mathbb{R},~ s>0.$

Keywords: nonlinear Schr\"odinger equation

MSC numbers: 5Q55, 35A05

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