Abstract theory of pointwise decay with applications to wave and Schr\"odinger equations

TL;DR

This paper develops an abstract conjugate operator method to establish pointwise decay estimates over time, and applies this framework to a broad class of dispersive wave and Schrödinger equations.

Contribution

Introduces a novel abstract conjugate operator approach for deriving decay estimates, applicable to various dispersive PDEs.

Findings

Established decay estimates for wave equations.

Extended decay results to Schrödinger equations.

Provided a unified framework for dispersive decay analysis.

Abstract

We prove pointwise in time decay estimates via an abstract conjugate operator method. This is then applied to a large class of dispersive equations.