Department of Mathematics

We’ll discuss long time decay estimates for the wave equation on a general class of asymptotically flat metrics. In the case of nontrapping metrics, when the operators are symmetric with slow time variation and a zero energy spectral condition, we’ll discuss local energy decay modulo finite dimensional dynamics. For a more general class of metrics, including black holes, we’ll discuss a general vector field method which takes local energy decay as an assumption. When used in combination, and also with the recent work of Dafermos, Rodnianski, and Shlapentokh-Rothman, these results establish a general asymptotic theory for both linear and null form equations on a wide variety of backgrounds. This is joint work with Jason Metcalfe, Jesus Oliver, Daniel Tataru. Tea at 3:33 pm in SC 1425. (Contact Person: Alex Powell)