Scattering theory for nls with inverse-square potential in 2d

2019/09/09 by Gao, Xiaofen, Xu, Chengbin
#35P25 #35Q55 #47J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.03572

Abstract

In this paper, we study the long time behavior of the solution of nonlinear Schrödinger equation with a singular potential. We prove scattering below the ground state for the radial NLS with inverse-square potential in dimension two iu_t+Δu-(a u)/(|x|²)= -|u|^pu when 20. This work extends the result in [13, 14, 16] to dimension 2D. The key point is a modified version of Arora-Dodson-Murphy's approach [2].

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