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Mostrando ítems 1-10 de 27
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
Uniqueness for SQG patch solutions
(American Mathematical Society, 2018-01)
This paper is about the evolution of a temperature front governed by the surface quasi-geostrophic equation. The existence part of that program within the scale of Sobolev spaces was obtained by the third author (2008). ...
Artículo
Generalized surface quasi-geostrophic equations with singular velocities
(Wiley, 2012)
This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized ...
Artículo
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 ...
Artículo
Some recent results on the Muskat problem
(Cellule MathDoc, 2010)
We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the ...
Artículo
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 ...
Artículo
Splash singularity for water waves
(National Academy of Sciences, 2012-01-17)
We exhibit smooth initial data for the two-dimensional (2D) waterwave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical ...
Artículo
Interface evolution: water waves in 2-D
(Elsevier, 2010-01-15)
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients ...
Artículo
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 ...
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.