Construction of the free-boundary 3D incompressible Euler flow under limited regularity

2023/07/05 by Mustafa Sencer Aydın, Igor Kukavica, Aydin, Mustafa Sencer +5 · 2 citations
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2307.02201

openalex publication_date 2023/07/05 · openalex created_date 2023/07/07 · openalex updated_date 2026/08/01

Abstract

We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We construct unique local-in-time solutions in the Lagrangian setting for u₀ ∈ H^2.5+δ such that the Rayleigh-Taylor condition holds and curl u₀ ∈ H^2+δ in an arbitrarily small neighborhood of the free boundary. We show that the result is optimal in the sense that H^3+δ regularity of the Lagrangian deformation near the free boundary can be ensured if and only if initial vorticity has H^2+δ regularity of vorticity near the free boundary.

Cited by

• The TURBO method for well-posedness of the incompressible Euler equations in Sobolev spaces in any domain
• The Euler equations with variable coefficients

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