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Hyperbolic & Dispersive PDE Seminar

A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

Allen Fang, Princeton University

Location:  Hill 525
Date & time: Thursday, 03 November 2022 at 2:00PM - 3:00PM

The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

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