# LOCAL WELL-POSEDNESS FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL IN Hs

• Zhang, Shan (The College of Mathematical Sciences Yangzhou University) ;
• Liu, Zuhan (School of Mathematical Science Xuzhou Normal University) ;
• Lu, Zhongxue (School of Mathematical Science Xuzhou Normal University)
• Received : 2010.07.30
• Published : 2011.11.30

#### Abstract

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

#### Acknowledgement

Supported by : NSF of Jiangsu Province, Natural Science Foundation of China

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