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We study the hyperboloidal initial value problem for the one-dimensional wave equation perturbed by a smooth potential. We show that the evolution decomposes into a finite-dimensional spectral part and an infinite-dimensional radiation part. For the radiation part we prove a set of Strichartz estimates. As an application we study the long-time asymptotics of Yang-Mills fields on a wormhole spacetime.
We establish Strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a (time-dependent) self-similar potential. As an application we consider the critical wave equation and prove the asymptotic sta
We consider the solution operator for the wave equation on the flat Euclidean cone over the circle of radius $rho > 0$, the manifold $mathbb{R}_+ times mathbb{R} / 2 pi rho mathbb{Z}$ equipped with the metric $g(r,theta) = dr^2 + r^2 dtheta^2$. Using
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the wave speed u
We study the Schrodinger equation on a flat euclidean cone $mathbb{R}_+ times mathbb{S}^1_rho$ of cross-sectional radius $rho > 0$, developing asymptotics for the fundamental solution both in the regime near the cone point and at radial infinity. The
We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.