Year: 2025
Author: Ping Li, Zijun Wan, Hua Wang, Xiaohua Yao
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 1 : pp. 1–41
Abstract
This paper is concerned with the time decay estimates of the fourth
order Schrödinger operator $H = ∆^2+V (x)$ in dimension three, where $V (x)$ is
a real valued decaying potential. Assume that zero is a regular point or the
first kind resonance of $H,$ and $H$ has no positive eigenvalues, we established the
following time optimal decay estimates of $e^{−it H}$ with a regular term $H^{α/4}:$
When zero is the second or third kind resonance of $H,$ their decay will be
significantly changed. We remark that such improved time decay estimates
with the extra regular term $H^{α/4}$ will be interesting in the well-posedness and
scattering of nonlinear fourth order Schrödinger equations with potentials.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0018
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 1 : pp. 1–41
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 41
Keywords: Fourth order Schrödinger equation asymptotic expansions $L^1−L^∞$ decay estimate resonances.