The energy-critical nonlinear wave equation with an inverse-square potential

TL;DR

This paper investigates the energy-critical nonlinear wave equation with an inverse-square potential in 3D and 4D, establishing global existence and scattering results for both defocusing and focusing cases under certain conditions.

Contribution

It provides the first comprehensive analysis of the energy-critical nonlinear wave equation with inverse-square potential, including scattering results in both defocusing and focusing scenarios.

Findings

Global solutions exist and scatter in the defocusing case.

Scattering occurs below the ground state threshold in the focusing case.

The inverse-square potential's influence on wave behavior is characterized.

Abstract

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.