Decay for the wave and Schroedinger evolutions on manifolds with conical ends, Part I

TL;DR

This paper establishes global dispersive estimates for Schrödinger and wave equations on manifolds with conical ends, focusing on initial data with zero angular momentum, despite the presence of trapping in the Hamiltonian flow.

Contribution

It provides the first dispersive estimates for these evolutions on manifolds with conical ends under trapping conditions, specifically for zero angular momentum initial data.

Findings

Global dispersive estimates are proven for Schrödinger and wave evolutions.

Results apply to manifolds with conical ends with trapping Hamiltonian flow.

Estimates are obtained for initial data with zero angular momentum.

Abstract

Global in time dispersive estimates for the Schroedinger and wave evolutions are obtained on manifolds with conical ends whose Hamiltonian flow exhibits trapping. This paper deals with the case of initial data with "zero angular momentum".