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Mostrando ítems 11-20 de 37
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, ...
Artículo
On a singular incompressible porous media equation
(AIP Publishing, 2012-11)
This paper considers a family of active scalar equations with transport velocities which are more singular by a derivative of order β than the active scalar. We prove that the equations with 0 < β ≤ 2 are Lipschitz ill-posed ...
Artículo
Quantitative Hölder estimates for even singular integral operators on patches
(ScienceDirect, 2022-11-01)
In this paper we show a constructive method to obtain estimates of even singular integral operators on characteristic functions of domains with regularity, . This kind of functions were shown in first place to be ...
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 ...
Tesis Doctoral
Global regularity for incompressible fluid interfaces.
(2018-06-11)
Esta memoria esta dedicada al estudio de tres problemas de frontera libre dadas por interfases entre fluidos incompresibles: parche de temperatura en Boussinesq, parche de densidad en Navier-Stokes y el problema de Muskat. ...
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 ...