Global existence for quasilinear wave equations close to Schwarzschild

Hans Lindblad; Mihai Tohaneanu

doi:10.1080/03605302.2018.1476529

Global existence for quasilinear wave equations close to Schwarzschild

Hans Lindblad, Mihai Tohaneanu

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

In this article, we study the quasilinear wave equation (Formula presented.) where the metric g(u,t,x) is close (and asymptotically equal) to the Schwarzschild metric g(0,t,x). Under suitable assumptions of the metric coefficients, and assuming that the initial data for u is small enough, we prove global existence and decay of the solution u. The main technical result of the paper is a local energy estimate for the linear wave equation on metrics with slow decay to the Schwarzschild metric.

Original language	English
Pages (from-to)	893-944
Number of pages	52
Journal	Communications in Partial Differential Equations
Volume	43
Issue number	6
DOIs	https://doi.org/10.1080/03605302.2018.1476529
State	Published - Jun 3 2018

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Taylor & Francis Group, LLC.

Funding

H. L. is supported in part by NSF grant DMS-1500925. M. T. is supported in part by the NSF grant DMS–1636435.

Funders	Funder number
National Science Foundation (NSF)	1636435, DMS–1636435, DMS-1500925

Keywords

Quasilinear wave equation
Schwarzschild

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2018.1476529

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abstract = "In this article, we study the quasilinear wave equation (Formula presented.) where the metric g(u,t,x) is close (and asymptotically equal) to the Schwarzschild metric g(0,t,x). Under suitable assumptions of the metric coefficients, and assuming that the initial data for u is small enough, we prove global existence and decay of the solution u. The main technical result of the paper is a local energy estimate for the linear wave equation on metrics with slow decay to the Schwarzschild metric.",

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AU - Tohaneanu, Mihai

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AB - In this article, we study the quasilinear wave equation (Formula presented.) where the metric g(u,t,x) is close (and asymptotically equal) to the Schwarzschild metric g(0,t,x). Under suitable assumptions of the metric coefficients, and assuming that the initial data for u is small enough, we prove global existence and decay of the solution u. The main technical result of the paper is a local energy estimate for the linear wave equation on metrics with slow decay to the Schwarzschild metric.

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KW - Schwarzschild

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Global existence for quasilinear wave equations close to Schwarzschild

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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