Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations最新文献

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6 Decay Estimates for and (Theorems M2, M3) 和的衰减估计(定理M2, M3)
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引用次数: 0
10 Regge-Wheeler Type Equations 10 Regge-Wheeler型方程
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引用次数: 0
1 Introduction 1介绍
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引用次数: 0
List of Figures 数字一览表
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引用次数: 0
B Appendix to Chapter 8 B第八章的附录
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引用次数: 0
C Appendix to Chapter 9 C第九章的附录
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Appendix B 附录B
{"title":"Appendix B","authors":"","doi":"10.2307/j.ctv15r57cw.16","DOIUrl":"https://doi.org/10.2307/j.ctv15r57cw.16","url":null,"abstract":"","PeriodicalId":371134,"journal":{"name":"Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127236367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
List of Figures 数字一览表
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引用次数: 0
Decay Estimates for q (Theorem M1) q的衰减估计(定理M1)
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations Pub Date : 2020-12-15 DOI: 10.23943/PRINCETON/9780691212425.003.0005
S. Klainerman, J. Szeftel
{"title":"Decay Estimates for q (Theorem M1)","authors":"S. Klainerman, J. Szeftel","doi":"10.23943/PRINCETON/9780691212425.003.0005","DOIUrl":"https://doi.org/10.23943/PRINCETON/9780691212425.003.0005","url":null,"abstract":"This chapter examines the proof for Theorem M1, deriving decay estimates for the quantity q for k ≤ k\u0000 small + 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.","PeriodicalId":371134,"journal":{"name":"Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations","volume":"2003 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127323752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
GCM Procedure GCM过程
S. Klainerman, J. Szeftel
{"title":"GCM Procedure","authors":"S. Klainerman, J. Szeftel","doi":"10.2307/j.ctv15r57cw.13","DOIUrl":"https://doi.org/10.2307/j.ctv15r57cw.13","url":null,"abstract":"This chapter describes the general covariant modulation (GCM) procedure in detail. It considers an axially symmetric polarized spacetime region R foliated by two functions (u, s) such that: on R, (u, s) defines an outgoing geodesic foliation as in section 2.2.4. The chapter then outlines the elliptic Hodge lemma. It also looks at the deformations of S surfaces, frame transformations, and the existence of GCM spheres. It recalls the transformation formulas recorded in Proposition 2.90, before rewriting a subset of these transformations in a more useful form. In the proof of existence and uniqueness of GCMS, one needs, in addition to the equations derived so far, an equation for the average of α‎. Finally, the chapter discusses the construction of GCM hypersurfaces.","PeriodicalId":371134,"journal":{"name":"Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122016410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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