Splash singularity for water waves

Abstract

We exhibit smooth initial data for the 2D water wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water wave equation that start from a graph, turn over and collapse in a splash singularity (self intersecting curve in one point) in finite time.

19 pages, 4 figures

References in corpus (2)

• Global well-posedness of the 3-D full water wave problem
• Turning waves and breakdown for incompressible flows

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• Splash singularities for a general Oldroyd model with finite Weissenberg number
• Drag force in bimodal cubic-quintic nonlinear Schrödinger equation
• Splash singularity for the free boundary incompressible viscous MHD
• Splash singularities for the one-phase Muskat problem in stable regimes
• In search of local singularities in ideal potential flows with free surface
• Small scale creation for 2D free boundary Euler equations with surface tension
• Formulation of finite-time singularity for free-surface Euler equations