Title: Local energy estimates on black hole backgrounds

Date: 02/06/2019

Time: 4:10 PM - 5:00 PM

Place: C517 Wells Hall

Local energy estimates are a robust way to measure decay of solutions to linear wave equations. I will discuss several such results on black hole backgrounds, such as Schwarzschild, Kerr, and suitable perturbations converging at various rates, and briefly discuss applications to nonlinear problems. The most challenging geometric feature one needs to deal with is the presence of trapped null geodesics, whose presence yield unavoidable losses in the estimates. This is joint work with Lindblad, Marzuola, Metcalfe, and Tataru.