2001/09/23 by S. Klainerman, Sergiù Klainerman, Igor Rodnianski +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #advanced mathematical theories #gr-qc #math.AP #math.CA #math.DG
paper · pdf · doi:10.48550/arxiv.math/0109173
arxiv created 2001/09/23 · openalex publication_date 2001/09/23 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first in a series Of papers in which we initiate the study Of very rough solutions to the initial value problem for the Einstein Vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques Of energy estimates and Sobolev inequalities. Following our previous work on quasilinear wave equations we develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Thus our result requires only H2+ε regularity for the data. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of the Einstein equations.