1307.2392 (Roland Donninger et al.)

A vector field method on the distorted Fourier side and decay for wave
equations with potentials    [PDF]

Roland Donninger, Joachim Krieger

We study the Cauchy problem for the one-dimensional wave equation with an inverse square potential. We derive dispersive estimates, energy estimates, and estimates involving the scaling vector field, where the latter are obtained by employing a vector field method on the "distorted" Fourier side. Our results have immediate applications in the context of geometric evolution problems.

View original: http://arxiv.org/abs/1307.2392