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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)

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

Sergiu Klainerman

Jérémie Szeftel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691212425.003.0005

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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