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

Xiaofen Gao; Chengbin Xu

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arXiv · 1909.03572

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

Xiaofen Gao·Chengbin Xu

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Abstract

In this paper, we study the long time behavior of the solution of nonlinear Schr\"odinger equation with a singular potential. We prove scattering below the ground state for the radial NLS with inverse-square potential in dimension two $$iu_t+\Delta u-\frac{a u}{|x|^2}= -|u|^pu$$ when $2 0$. 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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Xiaofen Gao, Chengbin Xu. 2019-09-09. Scattering theory for nls with inverse-square potential in 2d. https://arxiv.org/abs/1909.03572

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