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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
On the Muskat problem: global in time results in 2D and 3D
(Johns Hopkins University Press, 2016-12)
This paper considers the three dimensional Muskat problem in the stable regime. We obtain a conservation law which provides an L2 maximum principle for the fluid interface. We also show global in time existence for strong ...
Artículo
A note on interface dynamics for convection in porous media
(Elsevier, 2008-07-15)
We study the fluid interface problem through porous media given by two incompressible 2-D fluids of different densities. This problem is mathematically analogous to the dynamics interface for convection in porous media, ...