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Listar Artículos (Análisis Matemático) por autor "Castro Martínez, Ángel"
Mostrando ítems 1-11 de 11
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Artículo
Breakdown of smoothness for the Muskat problem
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
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 ...
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Finite time singularities for water waves with surface tension
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 ...
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Incompressible flow in porous media with fractional diffusion
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (IOP Publishing, 2009-08)In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous ...
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Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
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 ...
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Singularity formations for a surface wave model
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco (IOP Publishing, 2010-11)In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This ...
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Some recent results on the Muskat problem
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco (Cellule MathDoc, 2010)We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by ...
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Splash singularities for the one-phase Muskat problem in stable regimes
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 ...
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Artículo
Splash singularity for water waves
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 ...
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Structural stability for the splash singularities of the water waves problem
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 ...
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Artículo
Turning waves and breakdown for incompressible flows
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. ...