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Artículo
On the global existence for the Muskat problem
(European Mathematical Society, 2013)
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, ...
Artículo
Breakdown of smoothness for the Muskat problem
(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.
Artículo
Porous media: the Muskat problem in 3D
(Mathematical Sciences Publishers, 2013)
The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, ...
Artículo
2º Congreso de Jóvenes Investigadores
(Real Sociedad Matematica Española, 2013)
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 ...