Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential

TL;DR

This paper establishes weighted-L^2 and Strichartz estimates for the Schrödinger and wave equations incorporating an inverse-square potential, advancing understanding of their dispersive properties.

Contribution

It introduces new spacetime weighted-L^2 estimates for these equations with inverse-square potentials, leading to derived Strichartz estimates.

Findings

Proved weighted-L^2 estimates for Schrödinger and wave equations with inverse-square potential.

Derived Strichartz estimates from the weighted-L^2 bounds.

Enhanced understanding of dispersive behavior in presence of inverse-square potential.

Abstract

We prove spacetime weighted-L^2 estimates for the Schrodinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.