A KIRCHOFF–SOBOLEV PARAMETRIX FOR THE WAVE EQUATION AND APPLICATIONS

DOI10.1142/S0219891607001203zbMath1148.35042arXivmath/0309463WikidataQ115245264 ScholiaQ115245264MaRDI QIDQ3502737

Sergiu Klainerman, Igor Rodnianski

Publication date: 20 May 2008

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309463

zbMATH Keywords

Lorentzian manifoldEinstein vacuum equationscovariant tensorial wave equations

Mathematics Subject Classification ID

Wave equation (35L05) PDEs in connection with relativity and gravitational theory (35Q75) PDEs with randomness, stochastic partial differential equations (35R60) Hyperbolic equations on manifolds (58J45)

Related Items (14)

Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations ⋮ A geometric perspective on the method of descent ⋮ Continuation criterion for solutions to the Einstein equations ⋮ Sharp \(L^1\) estimates for singular transport equations ⋮ Integral formula for the characteristic Cauchy problem on a curved background ⋮ On the global dynamics of Yang-Mills-Higgs equations ⋮ A generalized representation formula for systems of tensor wave equations ⋮ Reflections on the U(1) problem in general relativity ⋮ On breakdown criteria for nonvacuum Einstein equations ⋮ On the radius of injectivity of null hypersurfaces ⋮ On the breakdown criterion in general relativity ⋮ On the geometry of null cones in Einstein-vacuum spacetimes ⋮ Improved breakdown criterion for einstein vacuum equations in CMC gauge ⋮ Weakly regular \(T^2\)-symmetric spacetimes. The global geometry of future Cauchy developments

Cites Work

• The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties
• The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. II. Completion of proof
• Global existence of solutions of the Yang-Mills equations on globally hyperbolic four dimensional Lorentzian manifolds
• Causal geometry of Einstein-vacuum spacetimes with finite curvature flux
• Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\)
• Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
• The Large Scale Structure of Space-Time

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