A sharp counterexample to local existence of low regularity solutions to\n Einstein's equations in wave coordinates

2016/03/16 by Boris Ettinger, Hans Lindblad, Ettinger, Boris +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1603.05167

openalex publication_date 2016/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are concerned with how regular initial data have to be to ensure local\nexistence for Einstein's equations in wave coordinates. Klainerman-Rodnianski\nand Smith-Tataru showed that there in general is local existence for data in\nSobolev spaces H^s with regularity s>2. We give an example of data in Sobolev\nspaces with regularity s=2 for which there is no local solution in this space.\n

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