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

Mizutani, Haruya

doi:10.1090/proc/13729

Global-in-time smoothing effects for Schrödinger equations with inverse-square potentials
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by Haruya Mizutani PDF

Proc. Amer. Math. Soc. 146 (2018), 295-307 Request permission

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 T. A. Bui et al. (J. Differential Equations 262 (2017), 2771–2807). The proof employs a uniform resolvent estimate proved by Barceló, Vega, and Zubeldia (Adv. Math. 240 (2013), 636–671) an abstract perturbation method by Bouclet and Mizutani (preprint).

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