A priori estimates for a relativistic liquid with free surface boundary

2018/11/16 by Daniel Ginsberg, Ginsberg, Daniel
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1811.06915

openalex publication_date 2018/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove energy estimates for a relativistic free liquid body with sufficiently small fluid velocity in a general Einstein spacetime. These estimates control Sobolev norms of the fluid velocity and enthalpy in the interior as well as Sobolev norms of the second fundamental form on the boundary.

Citations

• Well-posedness for the motion of an incompressible liquid with free surface boundary
• Global solutions for the gravity water waves equation in dimension 3

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