Daniel Tataru

Abstract:   We consider the question of long time behavior for linear wave and Schroedinger equations in $R^n$ for long range perturbations of the flat metric. This is related to spectral theory in the case of time independent coefficients, and to the dynamics of small data solutions for nonlinear evolutions. We discuss a phase space approach to the construction of global in time outgoing parametrices, as well as the connection to localized energy estimates and Strichartz type estimates.