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Mostrando ítems 11-20 de 27
Artículo
Singularity formations for a surface wave model
(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 system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex ...
Artículo
Interface evolution: the Hele-Shaw and Muskat problems
(Princeton University, 2011)
We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy’s law. The free boundary is given by the discontinuity among the densities and viscosities of ...
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
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 ...
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
Splash singularities for the one-phase Muskat problem in stable regimes
(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 ...
Artículo
Contour dynamics for 2D active scalars
(European Mathematical Society, 2009-03)
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, ...
Artículo
Finite time singularities for water waves with surface tension
(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 ...
Artículo
Structural stability for the splash singularities of the water waves problem
(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 ...