Local decay estimates for the bi-Laplacian Nonautonomous Schrödinger equation

Abstract

In this paper, we establish local decay estimates for the bi-Laplacian Schrödinger equation with time-dependent (in particular, quasi-periodic) potentials in spatial dimension $n\ge 14$. Moreover, under stronger spectral regularity hypotheses, the same result can be extended to dimension $n\ge 9$. Our approach, based on asymptotic completeness and the existence of the channel wave operator, departs from standard resolvent-based methods. In addition, global-in-time Strichartz estimates are derived from the local decay estimates.

49 pages, Comments welcome!