Formulation of finite-time singularity for free-surface Euler equations

TL;DR

This paper presents a concise proof demonstrating that free-surface incompressible Euler equations can develop finite-time singularities in two or three dimensions, offering a simplified perspective on a complex fluid dynamics problem.

Contribution

It provides an extremely short proof of finite-time singularity formation for free-surface Euler equations, simplifying previous complex analyses.

Findings

Finite-time singularity can occur in 2D and 3D free-surface Euler flows.

The proof is notably concise and straightforward.

Supports prior studies on singularity formation in fluid dynamics.

Abstract

We give an extremely short proof that the free-surface incompressible, irrotational Euler equations with regular initial condition can form a finite time singularity in 2D or 3D. Thus, we provide a simple view of the problem studied by Castro, Cordoba, Fefferman, Gancedo, Lopez-Fernadez, Gomez-Serrano and Coutand, Shkoller.