A Kirchoff-Sobolev parametrix for the wave equation and applications

2006/03/01 by S. Klainerman, Sergiù Klainerman, Igor Rodnianski +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Image and Signal Denoising Methods #Mathematical Physics (math-ph) #Numerical methods in engineering #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.math/0603009

arxiv created 2006/03/01 · openalex publication_date 2006/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a geometric construction of a first order physical space parametrix for solutions to covariant, tensorial wave equations on a curved background. We describe its applications to a large data breakdown criterion in General Relativity and also give a new gauge independent proof of the Eardley-Moncrief result on large data global existence result for the 3+1-dimensional Yang-MIlls equations.

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