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Mostrando ítems 21-27 de 27
Artículo
Turning waves and breakdown for incompressible flows
(National Academy of Sciences, 2011-03-22)
We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial ...
Artículo
Absence of squirt singularities for the multi-phase Muskat problem
(Springer, 2010-10)
In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove ...
Artículo
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
(Princeton University, 2012)
The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor ...
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Artículo
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 ...
Artículo
Lack of uniqueness for weak solutions of the incompressible porous media equation
(Springer, 2011-06)
In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz´ekelyhidi we prove non-uniqueness for solutions in L∞ in space and time.
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 ...