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Browsing by Author "Córdoba Gazolaz, Diego"
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A maximum principle for the Muskat problem for fluids with different densities [Article]
Córdoba Gazolaz, Diego; Gancedo García, Francisco (Springer, 200903)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 ...

A note on interface dynamics for convection in porous media [Article]
Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (Elsevier, 20080715)We study the fluid interface problem through porous media given by two incompressible 2D fluids of different densities. This problem is mathematically analogous to the dynamics interface for convection in porous media, ...

Absence of squirt singularities for the multiphase Muskat problem [Article]
Córdoba Gazolaz, Diego; Gancedo García, Francisco (Springer, 201010)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 (multiphase) HeleShaw problems. In this context we prove ...

Analytical behavior of twodimensional incompressible flow in porous media [Article]
Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (AIP Publishing (American Institute of Physics), 200706)In this paper we study the analytic structure of a twodimensional mass balance equation of an incompressible fluid in a porous medium given by Darcy’s law. We obtain local existence and uniqueness by the particletrajectory ...

Breakdown of smoothness for the Muskat problem [Article]
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco (Springer, 201306)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.

Contour dynamics for 2D active scalars [Presentation]
Córdoba Gazolaz, Diego; Gancedo García, Francisco (2010) 
Contour dynamics for 2D active scalars [Article]
Córdoba Gazolaz, Diego; Gancedo García, Francisco (European Mathematical Society, 200903) 
Contour dynamics of incompressible 3D fluids in a porous medium with different densities [Article]
Córdoba Gazolaz, Diego; Gancedo García, Francisco (Springer, 200707)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 twophase ...

Finite time singularities for the free boundary incompressible Euler equations [Article]
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; Gómez Serrano, Javier (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 ...

Finite time singularities for water waves with surface tension [Article]
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; Gómez Serrano, Javier (AIP Publishing, 201211)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 ...

Generalized surface quasigeostrophic equations with singular velocities [Article]
Chae, Dongho; Constantin, Peter; Córdoba Gazolaz, Diego; Gancedo García, Francisco; Wu, Jiahong (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 ...

Incompressible flow in porous media with fractional diffusion [Article]
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (IOP Publishing, 200908)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 ...

Interface evolution: the HeleShaw and Muskat problems [Article]
Córdoba Barba, Antonio; Córdoba Gazolaz, Diego; Gancedo García, Francisco (Princeton University, 2011)We study the dynamics of the interface between two incompressible 2D 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 ...

Interface evolution: water waves in 2D [Article]
Córdoba Barba, Antonio; Córdoba Gazolaz, Diego; Gancedo García, Francisco (Elsevier, 20100115)We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2D without surface tension. We prove localexistence in Sobolev spaces when, initially, the difference of the gradients ...

Lack of uniqueness for weak solutions of the incompressible porous media equation [Article]
Córdoba Gazolaz, Diego; Faraco Hurtado, Daniel; Gancedo García, Francisco (Springer, 201106)In this work we consider weak solutions of the incompressible 2D porous media equation. By using the approach of De LellisSz´ekelyhidi we prove nonuniqueness for solutions in L∞ in space and time.

On the global existence for the Muskat problem [Article]
Constantin, Peter; Córdoba Gazolaz, Diego; Gancedo García, Francisco; Strain, Robert M. (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, ...

On the Muskat problem: global in time results in 2D and 3D [Article]
Constantin, Peter; Córdoba Gazolaz, Diego; Gancedo García, Francisco; Rodríguez Piazza, Luis; Strain, Robert M. (Johns Hopkins University Press, 201612)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 ...

Porous media: the Muskat problem in 3D [Article]
Córdoba Barba, Antonio; Córdoba Gazolaz, Diego; Gancedo García, Francisco (Mathematical Sciences Publishers, 2013)The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3D the relevance of the RayleighTaylor condition, and the topology of the initial interface, ...

RayleighTaylor breakdown for the Muskat problem with applications to water waves [Article]
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco; López Fernández, María (Princeton University, 2012)The Muskat problem models the evolution of the interface between two different fluids in porous media. The RayleighTaylor condition is natural to reach linear stability of the Muskat problem. We show that the RayleighTaylor ...

Singularity formations for a surface wave model [Article]
Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco (IOP Publishing, 201011)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 ...