Scattering theory for subcritical wave equation with inverse square potential

TL;DR

This paper develops a scattering theory for subcritical wave equations with inverse square potential, demonstrating that radial solutions with finite energy scatter to free waves outside light cones using energy flux, characteristic line, and Morawetz estimates.

Contribution

It introduces a comprehensive scattering framework for subcritical wave equations with inverse square potential, combining multiple analytical techniques.

Findings

Radial finite-energy solutions scatter to free waves outside light cones.

Energy flux estimates are established on the light cone.

Scattering theory is extended to solutions with finite weighted energy initial data.

Abstract

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic line method and radiation theorem, we show that the radial finite-energy solutions scatter to free waves outside of light cones. Using Morawetz estimates we then obtain the scattering theory for radial solutions with finite weighted energy initial data.