Global existence for quasilinear wave equations close to Schwarzschild

DOI10.1080/03605302.2018.1476529zbMath1411.35209arXiv1610.00674OpenAlexW2962911272MaRDI QIDQ4622894

Hans Lindblad, Mihai Tohaneanu

Publication date: 18 February 2019

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.00674

zbMATH Keywords

quasilinear wave equationsmall initial dataSchwarzschild metriclocal energy estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with relativity and gravitational theory (35Q75) Initial value problems for second-order hyperbolic equations (35L15) Second-order quasilinear hyperbolic equations (35L72)

Related Items (16)

A large data theory for nonlinear wave on the Schwarzschild background ⋮ Linear stability of slowly rotating Kerr black holes ⋮ Global stability of Minkowski space for the Einstein-Maxwell-Klein-Gordon system in generalized wave coordinates ⋮ Pointwise decay for the wave equation on nonstationary spacetimes ⋮ Quasilinear wave equations on Schwarzschild–de Sitter ⋮ Global stability for charged scalar fields in an asymptotically flat metric in harmonic gauge ⋮ The effect of metric behavior at spatial infinity on pointwise wave decay in the asymptotically flat stationary setting ⋮ A local energy estimate for wave equations on metrics asymptotically close to Kerr ⋮ Boundedness and decay for the Teukolsky equation on Kerr spacetimes. I: The case \(|a|\ll M\) ⋮ A vector field method for radiating black hole spacetimes ⋮ Nonlinear stability for the Maxwell-Born-Infeld system on a Schwarzschild background ⋮ A sharp version of Price's law for wave decay on asymptotically flat spacetimes ⋮ Pointwise decay for semilinear wave equations on Kerr spacetimes ⋮ On a system of weakly null semilinear wave equations ⋮ Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field ⋮ Inverse problems for nonlinear hyperbolic equations with disjoint sources and receivers

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