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Browsing by Author "Gancedo García, Francisco"
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2º Congreso de Jóvenes Investigadores [Article]
Gancedo García, Francisco; Muro Jiménez, Fernando (Real Sociedad Matematica Española, 2013) 
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, ...

A survey for the Muskat problem and a new estimate [Article]
Gancedo García, Francisco (Springer, 201703)This paper shows a summary of mathematical results about the Muskat problem. The main concern is wellposed scenarios which include the possible formation of singularities in finite time or existence of solutions for all ...

Absence of splash singularities for surface quasigeostrophic sharp fronts and the Muskat problem [Article]
Gancedo García, Francisco; Strain, Robert M. (National Academy of Sciences (United States), 2014)In this paper, for both the sharp front surface quasigeostrophic equation and the Muskat problem, we rule out the “splash singularity” blowup scenario; in other words, we prove that the contours evolving from either of ...

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 ...

Existence for the αpatch model and the QG sharp front in Sobolev spaces [Article]
Gancedo García, Francisco (Elsevier, 20080401)We consider a family of contour dynamics equations depending on a parameter α with 0<α⩽1. The vortex patch problem of the 2D Euler equation is obtained taking α→0, and the case α=1 corresponds to a sharp front of the QG ...

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 ...

Global regularity for incompressible fluid interfaces. [PhD Thesis]
García Juárez, Eduardo Miguel (20180611)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 NavierStokes y el problema de Muskat. ...

Global regularity of 2D density patches for inhomogeneous NavierStokes [Article]
Gancedo García, Francisco; García Juárez, Eduardo Miguel (Springer, 2018)This paper is about Lions’ open problem on density patches: whether inhomogeneous incompressible NavierStokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev ...

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 ...