Title: Global dynamics for a class of inhomogeneous nonlinear Schr\"odinger equations with potential
Abstract: We consider a class of $L^2$-supercritical inhomogeneous nonlinear Schrodinger equations with potential in three dimensions
\[
i\partial_t u + \Delta u - V u = \pm |x|^{-b} |u|^\alpha u, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^3,
\]
where $0 \frac{4-2b}{3}$. In the focusing case, by adapting an argument of Dodson-Murphy, we first study the energy scattering below the ground state for the equation with radially symmetric initial data. We then establish blow-up criteria for the equation whose proof is based on an argument of Du-Wu-Zhang. In the defocusing case, we also prove the energy scattering for the equation with radially symmetric initial data.
Publication Year: 2019
Publication Date: 2019-09-27
Language: en
Type: preprint
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Cited By Count: 1
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