Global-in-time smoothing effects for Schrödinger equations with inverse-square potentials

Abstract

The purpose of this note is to prove global-in-time smoothing effects for the Schrödinger equation with potentials exhibiting critical singularity. A typical example of admissible potentials is the inverse-square potential $a|x{|}^{-2}$ with $a>-(n-2{)}^2/4$. This particularly gives an affirmative answer to a question raised by Bui-D'Ancona-Duong-Li-Ly [4]. The proof employs a uniform resolvent estimate proved by Barceló-Vega-Zubeldia [1] and an abstract perturbation method by Bouclet-Mizutani [3].

12 pages; revised version; title and abstract changed

References in corpus (1)

• Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential