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arXiv · 1204.6633

Finite time singularities for water waves with surface tension

Angel Castro·Diego Córdoba·Charles Fefferman·Francisco Gancedo·Javier Gómez-Serrano
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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.

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Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier Gómez-Serrano. 2012-04-30. Finite time singularities for water waves with surface tension. https://doi.org/10.1063/1.4765339

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