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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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# Consequences of the Bootstrap Assumptions

Chapter:
(p.145) Chapter Four Consequences of the Bootstrap Assumptions
Source:
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691212425.003.0004

This chapter discusses the proof for Theorem M0, together with other first consequences of the bootstrap assumptions. The only bootstrap assumption used in the proof of Theorem M0 is the bootstrap assumption BA-D on decay for k = 0, 1 derivatives. The chapter then relies on (4.1.5) and the assumptions (4.1.1) on the initial data layer. This observation allows one to use the conclusions of Theorem M0, not only for the bootstrap spacetime M in Theorem M1–M5, but also for the extended spacetime in the proof of Theorem M8, where the only assumption is the one on decay (which is established for the extended spacetime in Theorem M7). The chapter not only improves the bootstrap assumption (4.1.7), but also gains derivatives iteratively.

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