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Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations(AMS-210)$
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Jérémie Szeftel and Sergiu Klainerman

Print publication date: 2020

Print ISBN-13: 9780691212425

Published to Princeton Scholarship Online: May 2021

DOI: 10.23943/princeton/9780691212425.001.0001

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Decay Estimates for q (Theorem M1)

Decay Estimates for q (Theorem M1)

(p.213) Chapter Five Decay Estimates for q (Theorem M1)
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations

Sergiu Klainerman

Jérémie Szeftel

Princeton University Press

This chapter examines the proof for Theorem M1, deriving decay estimates for the quantity q for kksmall + 20 derivatives. To this end, it uses the wave equation satisfied by q. The spacetime M is decomposed as M = (int)M u (ext)M and that u is an outgoing optical function on (ext)M while u is an ingoing optical function. The chapter relies on the global frame defined in section 3.5, and r and m denote the corresponding scalar functions associated to it. It also proves two theorems on improved weighted estimates, as well as flux decay estimates for q.

Keywords:   Theorem M1, decay estimates, wave equation, optical function, spacetime M, scalar functions, improved weighted estimates, flux decay estimates

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