Speaker：Xiaohua Yao（Central China Normal University）

Time：2021-09-14 9:00

Location：Tencent Meeting ID：417717845（No Password）

Abstract:

It was well-known that the Lp decay estimates of Schrödinger operators, is a widely studied topic, which specially plays an important role in the well-posedness of nonlinear dispersive equations and the long time (asymptotic) stability of solitary waves. In this talk, we will address some recent works on the time decay estimates of the higher order elliptic operators (poly-harmonic type) with the decay potentials. Our methods depend on the detailed analysis of free resolvent and spectral perturbation techniques, where the classifications of zero resonances and zero asymptotic expansions of resolvent are the basic parts, which are indispensable to establish all kinds of results with general potentials. This talk mainly bases on joint-works with Avy Soffer and students.