Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles

TL;DR

This paper extends scattering results for the energy critical non-linear wave equation to a new class of non star-shaped obstacles, using generalized multiplier methods tailored to obstacle geometry.

Contribution

It introduces a generalized multiplier approach to prove scattering for non star-shaped obstacles in 3+1 dimensions, expanding previous results beyond star-shaped cases.

Findings

Scattering established for illuminated from exterior obstacles

Generalized multipliers effectively handle complex geometries

Method extends known results to broader obstacle classes

Abstract

Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.