Finite time singularities for water waves with surface tension

Abstract

Here we consider the 2D free boundary incompressible Euler equation with surface tension. We prove that the surface tension does not prevent a finite time splash or splat singularity, i.e. that the curve touches itself either in a point or along an arc. To do so, the main ingredients of the proof are a transformation to desingularize the curve and a priori energy estimates.

32 pages, 2 figures

References in corpus (1)

• On the finite-time splash and splat singularities for the 3-D free-surface Euler equations

Cited by in corpus (7)

• On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof
• On the absence of "splash" singularities in the case of two-fluid interfaces
• A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension
• A priori estimates for the free-boundary Euler equations with surface tension in three dimensions
• On the mathematical description of time-dependent surface water waves
• Justification of Peregrine soliton from full water waves
• Small scale creation for 2D free boundary Euler equations with surface tension