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arXiv · 1808.02236

Focusing NLS with inverse square potential

Jiqiang Zheng
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Abstract

In this paper, we utilize the method in Dodson-Murphy [4] to establish the radial scattering result for the focusing nonlinear Schrödinger equation with inverse square potential $i\pa_tu-\la u=-|u|^{p-1}u$ in the energy space $H^1_a(\R^d)$ in dimensions $d\geq3$, which extends the result of [10,11] to higher dimensions cases but with radial initial data. The new ingredient is to establish the dispersive estimate for radial function and overcome the weak dispersive estimate when $a<0$.

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Jiqiang Zheng. 2018-08-07. Focusing NLS with inverse square potential. https://doi.org/10.1063/1.5054167

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