# Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

## TL;DR

This paper establishes weighted L^2 estimates and improved local smoothing and Strichartz estimates for the Klein-Gordon equation with inverse-square potential, enhancing understanding of its well-posedness and dispersive properties.

## Contribution

It introduces new weighted L^2 estimates and refines local smoothing and Strichartz estimates for the Klein-Gordon equation with singular inverse-square potentials.

## Key findings

- Weighted L^2 estimates for Klein-Gordon with inverse-square potential
- Well-posedness of the Cauchy problem with small perturbations
- Improved local smoothing and Strichartz estimates

## Abstract

We prove weighted $L^2$ estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and go on to discuss local smoothing and Strichartz estimates which improve previously known ones.