Asymptotics of non-linear and linear waves on asymptotically flat spacetimes in three space dimensions

The HADES seminar on Tuesday, April 25th will be at 3:30 pm in Room 740.

Speaker: Shi-Zhuo Looi

Abstract: In this talk, we start with basic examples of wave decay and then delve into the investigation of asymptotic expansions for both non-linear and linear wave propagation in asymptotically flat spacetimes, allowing for non-stationary spacetimes without spherical symmetry assumptions. The analysis encompasses Schwarzschild spacetime and Kerr spacetimes within the full subextremal range. We present an exposition of a novel approach combining either integrated local energy decay or the limiting absorption principle, the r^p method, and, from a spectral perspective, resolvent expansions near zero energy. Potential applications of this research include scenarios involving waves interacting with spatially-localized objects, such as solitons.

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