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Artículo
Finite time singularities for water waves with surface tension
(AIP Publishing, 2012-11)
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 ...
Artículo
Structural stability for the splash singularities of the water waves problem
(American Institute of Mathematical Sciences, 2014-12)
In this paper we show a structural stability result for water waves. The main motivation for this result is that we would like to exhibit a water wave whose interface starts as a graph and ends in a splash. Numerical ...
Artículo
Finite time singularities for the free boundary incompressible Euler equations
(Princeton University, 2013)
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the ...