Focusing intercritical NLS with inverse-square potential

ABSTRACT

We study the focusing nonlinear Schrödinger equation with inverse-square potential $i{\mathrm{\partial }}_{t}u+\mathrm{\Delta }u-\frac{a}{|x{|}^2}u+|u{|}^{p-1}u=0$with $a>-\frac{1}{4}$ and $\frac{3}{4}<p-1<4$ in three dimensions. In this paper we obtain blow-up and global existence criteria for the solution to (${\mathrm{N}\mathrm{L}\mathrm{S}}_a$) by the method from Duyckaerts-Roudenko [1], which extend a recent work of Killip-Murphy-Visan-Zheng [2] to above the threshold.

KEYWORDS:

• Global existence
• blow-up
• virial indentity
• inverse-square potential

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 35B44
• Secondary 35A01

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

J.L. was partly supported by the Natural Science Foundation of China (No. 12101604).