Now showing items 1-8 of 8

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      Breakdown of smoothness for the Muskat problem  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco (Springer, 2013-06)
      In this paper we show that there exist analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, i.e., no longer belongs to C4.
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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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      Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; López Fernández, María (Princeton University, 2012)
      The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor ...
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      Splash singularities for the one-phase Muskat problem in stable regimes  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco (Springer, 2016-10)
      This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is with a dry region, where the density and the viscosity are set equal to 0 (the gradient of the ...
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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 ...
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      Turning waves and breakdown for incompressible flows  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; López Fernández, María (National Academy of Sciences, 2011-03-22)
      We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial ...