Decomposition of global solutions of bi-laplacian Nonautonomous Schrödinger equations

2023/08/13 by Soffer, Avy, Wu, Jiayan, Wu, Xiaoxu +1
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.06856

Abstract

We study the bi-Laplacian Schrödinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions to such equations decompose asymptotically into a free wave and a weakly localized component in all space dimensions. Moreover, in dimensions n ≥ 9, we prove that the weakly localized component is in fact spatially localized. The proof is based on a suitably adapted construction of the Free Channel Wave Operator, building on the method recently developed in~\citeSW20221.

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