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      Finite time singularities for the free boundary incompressible Euler equations  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; Gómez Serrano, Javier (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 ...
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      Finite time singularities for water waves with surface tension  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; Gómez Serrano, Javier (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 ...
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      Splash singularity for water waves  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; Gómez Serrano, Javier (National Academy of Sciences, 2012-01-17)
      We exhibit smooth initial data for the two-dimensional (2D) waterwave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical ...
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      Structural stability for the splash singularities of the water waves problem  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; Gómez Serrano, Javier (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 ...