Einstein vacuum equations with \mathbbU(1) symmetry in an elliptic gauge : local well-posedness and blow-up criterium

2021/01/22 by Arthur Touati, Touati, Arthur
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2101.09093

openalex publication_date 2021/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we are interested in the Einstein vacuum equations on a Lorentzian manifold displaying \mathbbU(1) symmetry. We identify some freely prescribable initial data, solve the constraint equations and prove the existence of a unique and local in time solution at the H³ level. In addition, we prove a blow-up criterium at the H² level. Our main objective is to provide a framework adapted to the study of high-frequency solutions to the Einstein vacuum equations done in a forthcoming paper by Huneau and Luk. As a consequence we work in an elliptic gauge, particularly adapted to the handling of high-frequency solutions, which have large high-order norms.

Citations

• Partial Differential Equations

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