Mathematics

  1. On the dynamics of 3D electrified falling films, Submitted (with J. He).
  2. Well-posedness of the water-wave with viscosity problem , Submitted (with S. Scrobogna).
  3. Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems , Submitted (with H. Bae).
  4. Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium , To appear in Annales de l'Institut Henri Poincare / Analyse non lineaire (with F. Gancedo and S. Scrobogna).
  5. Global existence and exponential decay to equilibrium for DLSS-type equations , To appear in Journal of Dynamics and Differential Equations (with H. Bae).
  6. Well-posedness of a water wave model with viscous effects, To appear in Proceedings of the American Mathematical Society (with S. Scrobogna).
  7. On a nonlocal differential equation describing roots of polynomials under differentiation, To appear in Communications in Mathematical Sciences
  8. On an asymptotic model for free boundary Darcy flow in porous media, To appear in SIAM Journal on Mathematical Analysis (with S. Scrobogna).
  9. On a thin film model with insoluble surfactant, Journal of Differential Equations, vol. 268, n. 12, pp 7582-7608, 2020 (with G. Bruell).
  10. Models for damped water waves, SIAM Journal of Applied Mathematics, vol.79, n.6, pp. 2530-2550, 2019 (with S. Scrobogna)
  11. Asymptotic models for free boundary flow in porous media, Physica D, vol 392, pp. 1-16, 2019 (with S. Scrobogna).
  12. Growth in the Muskat problem, Mathematical Modelling of Natural Phenomena, vol. 15, 7, 2020 (with O. Lazar).
  13. Rigorous Asymptotic Models of Water Waves, Water Waves, vol. 1, n. 1, pp 71–130, 2019 (with A. Cheng, S. Shkoller and J. Wilkening).
  14. On the local and global existence of solutions to 1D transport equations with nonlocal velocity, Networks and Heterogeneous Media, vol 14. n.3, pp. 471-487, 2019. (with H. Bae and O. Lazar).
  15. Global existence and decay to equilibrium for some crystal surface models, Discrete and Continuous Dynamical Systems-A vol. 39, n. 4, pp. 2101-2131, 2019 (with M. Magliocca).
  16. On the thin film Muskat and the thin film Stokes equations, Journal of Mathematical Fluid Mechanics, vol 21. pp. 33, 2019. (with G. Bruell).
  17. Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations, Discrete and Continuous Dynamical Systems-S vol. 13, n. 2, pp. 139-164, 2019 (with J. Burczak).
  18. Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability, Transactions of the American Mathematical Society, vol 372, n. 4, pp. 2255–2286, 2019. (with S. Shkoller).
  19. Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation, Journal of Differential Equations vol. 263, n. 9, pp. 6115-6142, 2017 (with J. Burczak).
  20. Global existence of weak solutions to dissipative transport equations with nonlocal velocity, Nonlinearity, vol. 31, n.4, pp. 1484-1515, 2018 (with H. Bae and O. Lazar).
  21. Global solutions for a hyperbolic-parabolic system of chemotaxis, Journal of Mathematical Analysis and Applications, vol. 449, n.1, pp. 872-883, 2017.
  22. On the fractional Fisher information with applications to a hyperbolic-parabolic system of chemotaxis, Journal of Differential Equations, vol. 262, n. 4, pp. 3250-3283, 2017.
  23. A model for Rayleigh-Taylor mixing and interface turn-over, Multiscale Modeling and Simulation, vol. 15, n. 1, pp 274-308, 2017 (with S. Shkoller).
  24. On a drift-diffusion system for semiconductor devices, Annales Henri Poincaré, vol. 17, n. 12, pp 3473–3498, 2016.
  25. On a generalized Buckley-Leverett equation, Journal of Mathematical Physics, 57, 041501, 2016 (with J. Burczak and K. Luli).
  26. Global solutions for a supercritical drift-diffusion equation, Advances in Mathematics, 295, pp. 334-367, 2016 (with J. Burczak).
  27. Critical Keller-Segel meets Burgers on S1: large-time smooth solutions, Nonlinearity, vol. 29, n.12, pp. 3810, 2016 (with J. Burczak).
  28. Well-posedness of the Muskat problem with H2 initial data, Advances in Mathematics, 286, pp. 32-104, 2016 (with A. Cheng and S. Shkoller).
  29. Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux, Topological Methods in Nonlinear Analysis, vol. 47, n.1, pp 369-387, 2016 (with J. Burczak).
  30. On a generalized doubly parabolic Keller-Segel system in one spatial dimension, Mathematical Models and Methods in Applied Sciences, vol. 26, no. 1 pp. 111-160, 2016 (with J. Burczak).
  31. Global existence for some transport equations with nonlocal velocity, Advances in Mathematics, vol. 269, pp 197-219, 2015 (with H. Bae).
  32. On the effect of boundaries in two-phase porous flow, Nonlinearity vol. 28, n. 2, pp. 435-461, 2015 (with G. Navarro & A. Ortega).
  33. On a nonlocal analog of the Kuramoto-Sivashinsky equation, Nonlinearity vol. 28, n. 4, pp. 1103-1133, 2015 (with J. K. Hunter).
  34. On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof, Nonlinearity, vol. 27, n. 6, pp. 1471-1498, 2014 (with J. Gómez-Serrano).
  35. An aggregation equation with a nonlocal flux, Nonlinear Analysis Series A: Theory, Methods & Applications, vol. 108, pp. 260-274, 2014 (with R. Orive).
  36. Global existence for the confined Muskat problem, SIAM Journal on Mathematical analysis, vol. 46, n. 2, pp. 1651-1680, 2014.
  37. Local solvability and turning for the inhomogeneous Muskat problem, Interfaces and Free Boundaries, vol. 16, n.2, pp. 175-213, 2014 (with L. C. Berselli & D. Córdoba).
  38. An approximative treatment of gravitational collapse, Physica D: Nonlinear Phenomena, vol. 262, pp. 71-82, 2013 (with Y. Ascasíbar & J. M. Moreno).
  39. The confined Muskat problem: differences with the deep water regime, Communications in Mathematical Sciences, vol. 12, no. 3, pp. 423-455, 2014 (with D. Córdoba & R. Orive).
  40. New insight into Wolbachia epidemiology: its varying incidence during the host life cycle can alter bacteria spread, Bulletin of Mathematical Biology, vol. 76, n.10, pp. 2646-2663, 2014 (with P. Martínez, F. Arroyo-Yebras & J.L. Bella).
  41. Impact of the climatic change on animal diseases spread: the example of bluetongue in Spain, Revista Complutense de Ciencias Veterinarias, vol 5, num 1, pag 120-131, 2011 (with C. Cianci et. al.).

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Slides & Posters

  1. Slides of the talk 'New models for Euler flows with a free boundary: the Rayleigh-Taylor and Kelvin-Helmholtz instabilities', Bodega Marine Laboratory, Bodega bay, June 2017.
  2. Poster on the Rayleigh-Taylor instability and mixing 'The inhomogeneous Muskat problem', IMPAN, Warsaw, February 2017.
  3. Slides of the talk 'On the dynamics of free boundaries between incompressible fluids', King's College London, Londres, March 2016.
  4. Slides of the talk 'The inhomogeneous Muskat problem', Vanderbilt University, Nashville, May 2016.
  5. Slides of the talk 'On two nonlocal equations showing chaotic behaviour', Université Claude Bernard Lyon 1, Lyon, July 2015.
  6. Slides of the talk 'Dynamics of internal waves in inhomogeneous porous media', University of California at Berkeley, Berkeley, April 2014.
  7. A poster with some of the results for the Muskat problem. This poster was presented at EMS-RSME joint mathematical weekend 2011.
  8. Another poster with some of the results for the Muskat problem. This poster was presented at International winter school in fluid dynamics 2012.
  9. A poster summarizing our results for the Wolbachia infection. This poster was presented on the Third SESBE Congress.

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Popular Science & Outreach

  1. El Problema de Basilea: Historia y algunas demostraciones. La Gaceta de la RSME, vol 12, num 4, pag 721-737, 2009.
  2. La ecuación de Burgers como un paso previo al estudio de los fluidos incompresibles La Gaceta de la RSME, vol 15, num 3, pag, 489-512, 2012 (with José Manuel Moreno).

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