Wednesday, July 10, 2013

1307.2392 (Roland Donninger et al.)

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

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.
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