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arXiv · 1801.05165

Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential

Qing Guo·Hua Wang·Xiaohua Yao
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Abstract

In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear Schr\"{o}dinger equation with a potential $$ iu_{t}+\Delta u-Vu+|x|^{-b}|u|^{2}u=0,\;\;(t,x) \in {{\bf{R}}\times{\bf{R}}^{3}}, $$ where $0 \mathcal{K}$ if $V$ satisfies some additional assumptions.0}\|_{L^{2}}^{2(1-s_{c})}\|H^{\frac{1}{2}}u_{0}\|_{L^{2}}^{2s_{c}}>\mathcal{K}$ if $V$ satisfies some additional assumptions.

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Qing Guo, Hua Wang, Xiaohua Yao. 2018-01-16. Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential. https://arxiv.org/abs/1801.05165

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