Global solvabilty for nonlinear wave equations with singular potential

TL;DR

This paper proves the global existence of solutions for 3D semilinear wave equations with certain singular potentials, using conformal energy estimates and Hardy inequalities, especially in the supercritical case.

Contribution

It introduces a novel approach combining conformal energy estimates and Hardy inequalities to establish global existence for wave equations with singular potentials.

Findings

Global existence for small data in supercritical case

Effective use of conformal energy estimates and Hardy inequalities

Applicable to wave equations with decay-satisfying potentials

Abstract

In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case we establish the small data global existence result. The approach is based on appropriate conformal energy estimate in combination with Hardy inequality for conformal energy on space - like surfaces.