Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates

TL;DR

This paper establishes local decay estimates for the semilinear wave equation on the Schwarzschild manifold, providing a foundation for understanding wave behavior in curved spacetime.

Contribution

It introduces Morawetz type estimates for non-radial data on the Schwarzschild manifold, advancing the analysis of wave decay in general relativity.

Findings

Proved local decay estimates for the wave equation on Schwarzschild

Derived a-priori Morawetz type estimates for non-radial data

Enhanced understanding of wave behavior in curved spacetime environments

Abstract

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.