Papers

  1. Contour dynamics of incompressible 3-D fluids in a porous medium with different densities, with D. Córdoba.
    Comm. Math. Phys., 273, no. 2, 445-471 (2007).

  2. Analytical behavior of 2D incompressible flow in porous media, with D. Córdoba and R. Orive.
    J. Math. Phys., 48, no. 6 (2007).

  3. Existence for the $\alpha$-patch model and the QG sharp front in Sobolev spaces.
    Adv. Math., 217, no. 6, 2569-2598 (2008).

  4. A maximum principle for the Muskat problem for fluids with different densities, with D. Córdoba.
    Comm. Math. Phys., 286, no. 2, 681-696 (2009).

  5. A note on the interface dynamics for convection in porous media, with D. Córdoba and R. Orive.
    Physica D, 237, no. 10-12, 1488-1497 (2008).

  6. Incompressible flow in porous media with fractional diffusion, with A. Castro, D. Córdoba and R. Orive.
    Nonlinearity, 22, no. 8, 1791-1815 (2009).

  7. Interface evolution: the Hele-Shaw and Muskat problems, with A. Córdoba and D. Córdoba.
    Annals of Math, 173, no. 1, 477-542 (2011).

  8. The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces, with A. Córdoba and D. Córdoba.
    Proc. Natl. Acad. Sci., 106, no. 27, 10955-10959 (2009).

  9. Interface evolution: water wave in 2-D, with A. Córdoba and D. Córdoba.
    Adv. Math., 223, no. 1, 120-173 (2009).

  10. Contour dynamics for 2D active scalars, with D. Córdoba.
    Newsletter of the European Mathematical Society, no. 71 (March 2009).

  11. Absence of squirt singularities for the multi-phase Muskat problem, with D. Córdoba.
    Comm. Math. Phys., 299, no. 2, 561-575 (2010).

  12. Lack of uniqueness for weak solutions of the incompressible porous media equation, with D. Córdoba and D. Faraco.
    Arch. Ration. Mech. Anal., 200, no. 3, 725-746 (2011).

  13. A naive parametrization for the vortex-sheet problem, with A. Castro and D. Córdoba.
    ArXiv:0810.0731 (2010).

  14. Singularity Formation in a Surface Wave Model, with A. Castro and D. Córdoba.
    Nonlinearity, 23, no. 11, 2835-2847 (2010).

  15. Porous media: the Muskat problem in 3D, with A. Córdoba and D. Córdoba.
    Submitted (2010).

  16. On the global existence for the Muskat problem, with P. Constantin, D. Córdoba and R. M. Strain.
    To appear in JEMS (2011).

  17. Some recent results on the Muskat problem, with A. Castro and D. Córdoba.
    Journees Equations aux Derivees Partielles (2010).

  18. Turning waves and breakdown for incompressible flows, with A. Castro, D. Córdoba, C. Fefferman and M. López-Fernández.
    Proc. Natl. Acad. Sci. 108, no. 12, 4754-4759 (2011).

  19. Generalized surface quasi-geostrophic equations with singular velocities, with D. Chae, P. Constantin, D. Córdoba and J. Wu.
    Submitted (2011).

  20. Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, with A. Castro, D. Córdoba, C. Fefferman and M. López-Fernández.
    To appear in Annals of Math (2011).

  21. Breakdown of smoothness for the Muskat problem, with A. Castro, D. Córdoba and C. Fefferman.
    Preprint (2010).

  22. Splash singularity for water waves, with A. Castro, D. Córdoba, C. Fefferman and J. Gómez-Serrano.
    Submitted (2011).