January 24, 2008

Jeremy Marzuola (Columbia University)

Title: Strichartz Estimates and Local Smoothing Estimates for Asymptotically Flat Schr\"odinger Equations

Abstract: With Jason Metcalfe and Daniel Tataru, we study global-in-time Strichartz estimates for the Schr\"odinger evolution corresponding to long-range perturbations of the Euclidean Laplacian. We consider the case of large perturbations as an extension of the work of Tataru, who showed with a particular parametrix construction that global in time Strichartz estimates follow from local smoothing estimates under certain non-trapping/smallness conditions. In our case, we show similar estimates with an extra spatially localized error term.