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Now showing items 1-8 of 8
Article
The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
(National Academy of Sciences, 2009-07-07)
For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially ...
Article
Analytical behavior of two-dimensional incompressible flow in porous media
(AIP Publishing (American Institute of Physics), 2007-06)
In this paper we study the analytic structure of a two-dimensional mass balance equation of an incompressible fluid in a porous medium given by Darcy’s law. We obtain local existence and uniqueness by the particle-trajectory ...
Article
Incompressible flow in porous media with fractional diffusion
(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 medium governed by Darcy’s law. We show formation of singularities with infinite energy and for finite ...
Article
A maximum principle for the Muskat problem for fluids with different densities
(Springer, 2009-03)
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two ...
Article
Contour dynamics for 2D active scalars
(European Mathematical Society, 2009-03)
Article
Existence for the α-patch model and the QG sharp front in Sobolev spaces
(Elsevier, 2008-04-01)
We consider a family of contour dynamics equations depending on a parameter α with 0<α⩽1. The vortex patch problem of the 2-D Euler equation is obtained taking α→0, and the case α=1 corresponds to a sharp front of the QG ...
Article
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, ...
Article
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
(Springer, 2007-07)
We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase ...