• Corpus ID: 233864907

Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials

@inproceedings{Cheng2021ScatteringOT,
  title={Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials},
  author={Xing Cheng and Chang-Yu Guo and Zihua Guo and Xian Liao and Jia Shen},
  year={2021}
}
In this paper, we consider the following three dimensional defocusing cubic nonlinear Schr\"odinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2 u, \quad u|_{t=0} = u_0. \end{equation*} Our main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approximate (NLS) in the large-scale case by a relevant… 
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