Pointwise decay for semilinear wave equations on Kerr spacetimes

Abstract

In this article we prove optimal pointwise bounds for solutions to the semilinear wave equation with integer powers p ≥ 3 on Kerr backgrounds with small angular momentum and small initial data.

Sharp decay for Teukolsky equation in Kerr spacetimes

“…For large initial data, see [41]. Quite recently, Tohaneanu [94] proved the optimal pointwise upper bounds t −1 t − r −κ with p ≥ 3 and κ = min{2, p − 2} for solutions arsing from small initial data in Kerr spacetimes. The second model problem (1.19) is a prototye of wave equations respecting the null condition [58,24].…”

“…Looi [64] obtained pointwise decay estimates for solutions to linear wave equations with variable coefficients. Tohaneanu [94] proved the sharp upper bound of pointwise decay for a semilinear wave equation on a slowly rotating Kerr background.…”