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

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.

To appear in Discrete Contin. Dyn. Syst., 13 pages