Now showing items 1-20 of 27

    • Icon

      A maximum principle for the Muskat problem for fluids with different densities  [Article]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco (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 ...
    • Icon

      A note on interface dynamics for convection in porous media  [Article]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (Elsevier, 2008-07-15)
      We study the fluid interface problem through porous media given by two incompressible 2-D fluids of different densities. This problem is mathematically analogous to the dynamics interface for convection in porous media, ...
    • Icon

      Absence of squirt singularities for the multi-phase Muskat problem  [Article]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco (Springer, 2010-10)
      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 (multi-phase) Hele-Shaw problems. In this context we prove ...
    • Icon

      Analytical behavior of two-dimensional incompressible flow in porous media  [Article]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (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 ...
    • Icon

      Breakdown of smoothness for the Muskat problem  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Fefferman, Charles L.; Gancedo García, Francisco (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.
    • Icon

      Contour dynamics for 2D active scalars  [Presentation]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco (2010)
    • Icon

      Contour dynamics for 2D active scalars  [Article]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco (European Mathematical Society, 2009-03)
    • Icon

      Contour dynamics of incompressible 3-D fluids in a porous medium with different densities  [Article]

      Córdoba Gazolaz, Diego; Gancedo García, Francisco (Springer, 2007-07)
      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 two-phase ...
    • Icon

      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 ...
    • Icon

      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, 2012-11)
      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 ...
    • Icon

      Generalized surface quasi-geostrophic 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 ...
    • Icon

      Incompressible flow in porous media with fractional diffusion  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco; Orive Illera, Rafael (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 ...
    • Icon

      Interface evolution: the Hele-Shaw 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 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 ...
    • Icon

      Interface evolution: water waves in 2-D  [Article]

      Córdoba Barba, Antonio; Córdoba Gazolaz, Diego; Gancedo García, Francisco (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 ...
    • Icon

      Lack of uniqueness for weak solutions of the incompressible porous media equation  [Article]

      Córdoba Gazolaz, Diego; Faraco Hurtado, Daniel; Gancedo García, Francisco (Springer, 2011-06)
      In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz´ekelyhidi we prove non-uniqueness for solutions in L∞ in space and time.
    • Icon

      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, ...
    • Icon

      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, 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 ...
    • Icon

      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 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, ...
    • Icon

      Rayleigh-Taylor 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 Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor ...
    • Icon

      Singularity formations for a surface wave model  [Article]

      Castro Martínez, Ángel; Córdoba Gazolaz, Diego; Gancedo García, Francisco (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 ...