Buscar
Mostrando ítems 1-10 de 26
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
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
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
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.
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, ...