Wave equations on space-times of low regularity: Existence results and regularity theory in the framework of generalized function algebras

TL;DR

This paper explores the existence and regularity of solutions to wave equations on singular space-times within the framework of generalized function algebras, advancing Lorentzian geometry and regularity theory.

Contribution

It introduces a novel approach to analyze wave equations on low-regularity space-times using generalized function algebras, expanding the understanding of Lorentzian geometry in singular settings.

Findings

Development of regularity results for wave equations on singular space-times

Application of generalized function algebras to Lorentzian geometry

Enhanced understanding of wave propagation in low-regularity geometries

Abstract

We present recent developments concerning Lorentzian geometry in algebras of generalized functions. These have, in particular, raised a new interest in refined regularity theory for the wave equation on singular space-times.