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

2023/07/05 by Aydin, Mustafa Sencer, Kukavica, Igor, Ożański, Wojciech S. +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.02201

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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