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 Local well-posedness for the nonlinear Schr\"odinger equation with harmonic potentila in $H^s$ Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1291-1302 https://doi.org/10.4134/BKMS.2011.48.6.1291Published online November 1, 2011 Shan Zhang, Zuhan Liu, and Zhongxue L\"u Yangzhou University, Xuzhou Normal University, Xuzhou Normal University Abstract : 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 Full-Text :