Local energy decay and the vector field method

DOI10.2969/aspm/08510369zbMath1469.35041OpenAlexW3140668120MaRDI QIDQ2042475

Jacob Sterbenz

Publication date: 20 July 2021

Full work available at URL: https://doi.org/10.2969/aspm/08510369

zbMATH Keywords

Morawetz estimateKlainerman vector field method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15) Second-order semilinear hyperbolic equations (35L71)

Cites Work

• The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes
• Global parametrices and dispersive estimates for variable coefficient wave equations
• On the asymptotic behavior of solutions to the Einstein vacuum equations in wave coordinates
• Hyperbolic trapped rays and global existence of quasilinear wave equations
• Spectral theory of the Klein-Gordon equation in Pontryagin spaces
• The global stability of Minkowski space-time in harmonic gauge
• Strichartz estimates on Schwarzschild black hole backgrounds
• The \(r^{p}\)-weighted energy method of Dafermos and Rodnianski in general asymptotically flat spacetimes and applications
• A vector field method approach to improved decay for solutions to the wave equation on a slowly rotating Kerr black hole
• A vector field method for radiating black hole spacetimes
• Global existence of null-form wave equations in exterior domains
• A Local Energy Estimate on Kerr Black Hole Backgrounds
• Local energy decay for scalar fields on time dependent non-trapping backgrounds
• Decay for solutions of the exterior problem for the wave equation
• Time decay for the nonlinear Klein-Gordon equation
• Exponential decay of solutions of the wave equation

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