Nonscattering range for the NLS with inverse square potential

We establish that scattering for the defocusing nonlinear Schrodinger equations with inverse square potential iu(t) - L(a)u = vertical bar u vertical bar(p)u cannot occur if 1 < p <= 1 + 2/3 in dimension three with L-a := -Delta+a/vertical bar x vertical bar(2) . The main tools are Hankel transform, Bessel function and the dispersive estimate. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

Using Hankel transform, Bessel function and the dispersive estimate, we establish that scattering does not occur for defocusing nonlinear Schrodinger equations with inverse square potential in three dimensions under certain conditions.