Papers

  1. Existence of analytic non-convex V-states, with G. Castro-López.
    Submitted (2024).

  2. A note on the periodic Hilbert Transform on a strip, with S. Kim.
    Submitted (2024).

  3. Non-radial implosion for the defocusing nonlinear Schrödinger equation in Td and Rd, with G. Cao-Labora, J. Shi and G. Staffilani.
    Submitted (2024).

  4. Non-radial implosion for compressible Euler and Navier-Stokes in T3 and R3, with G. Cao-Labora, J. Shi and G. Staffilani.
    Submitted (2023).

  5. Desingularization of small moving corners for the Muskat equation, with E. García-Juárez, S. V. Haziot and B. Pausader.
    Annals of PDE, 10, 17 (2024).

  6. Quasiperiodic solutions of the generalized SQG equation, with A. Ionescu and J. Park.
    Annals of Mathematics Studies, to appear.

  7. Smooth self-similar imploding profiles to 3D compressible Euler, with T. Buckmaster and G. Cao-Labora.
    Quarterly of Applied Mathematics, 81, 517-532 (2023).

  8. Smooth imploding solutions for 3D compressible fluids, with T. Buckmaster and G. Cao-Labora.
    Forum of Mathematics Pi, to appear.

  9. Self-similar spirals for the generalized surface quasi-geostrophic equations, with C. García.
    Journal of the European Mathematical Society, to appear.

  10. Highest Cusped Waves for the Burgers-Hilbert equation, with J. Dahne.
    Arch. Ration. Mech. Anal., 247, 74 (2023).

  11. Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networks, with T. Buckmaster, C.Y. Lai and Y. Wang.
    Physical Review Letters, 130, no. 24, 244002 (2023).

    Quanta Magazine: Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations.
    El País: Encuentran una explosión en las ecuaciones de los fluidos gracias al aprendizaje profundo.

  12. Existence of non-trivial non-concentrated compactly supported
    stationary solutions of the 2D Euler equation with finite energy    , with J. Park and J. Shi.
    Memoirs of the AMS, to appear.

  13. Self-similar solutions for the Muskat equation, with E. García-Juárez, H. Q. Nguyen and B. Pausader.
    Advances in Mathematics, 399, 108294 (2022).

  14. A counterexample to Payne’s nodal line conjecture with few holes, with J. Dahne and K. Hou.
    Commun. Nonlinear Sci. Numer. Simul., 103, 105957 (2021).
    Special Issue “Computer Assisted Proofs in Dynamical Systems”.

  15. Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results, with J. Park, J. Shi and Y. Yao.
    Phil. Trans. R. Soc. A, 380, no. 2226, 20210045 (2022).

  16. Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results, with J. Park, J. Shi and Y. Yao.
    Communications in Mathematical Physics, 386, 1845–1879 (2021).

  17. Any three eigenvalues do not determine a triangle, with G. Orriols.
    Journal of Differential Equations, 275, 920-938 (2021).

  18. Symmetry in stationary and uniformly-rotating solutions of active scalar equations, with J. Park, J. Shi and Y. Yao.
    Duke Mathematical Journal, 170, no. 13, 2957-3038 (2021).

  19. Convexity of Whitham’s highest cusped wave, with A. Enciso and B. Vergara.
    Submitted (2018).

  20. Computer-assisted proofs in PDE: a survey.
    SeMA Journal, 76, no. 3, 459-484 (2019).

  21. On the existence of stationary patches.
    Advances in Mathematics, 343, 110-140 (2019).

  22. Spectral determination of semi-regular polygons, with A. Enciso.
    Journal of Differential Geometry, 122 (3), 399-419 (2022).

  23. Global solutions for the generalized SQG patch equation, with D. Córdoba and A. Ionescu.
    Arch. Ration. Mech. Anal., 233, no. 3, 1211-1251 (2019).

  24. Uniformly rotating smooth solutions for the incompressible 2D Euler equations, with A. Castro and D. Córdoba.
    Arch. Ration. Mech. Anal., 231, no. 2, 719-785 (2019).

  25. Global smooth solutions for the inviscid SQG equation, with A. Castro and D. Córdoba.
    Memoirs of the AMS, 266, 1292, 89 pp (2020).

  26. A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable, with D. Córdoba and A. Zlatoš.
    Analysis & PDE, 10, no. 2, 367-378 (2017).

  27. Uniformly rotating analytic global patch solutions for active scalars, with A. Castro and D. Córdoba.
    Annals of PDE, 2, no. 1, 1-34 (2016).

  28. Splash singularities for the free boundary Navier-Stokes equations, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.
    Annals of PDE, 5, no. 1, 5:12 (2019).

  29. A note on stability shifting for the Muskat problem, with D. Córdoba and A. Zlatoš.
    Phil. Trans. R. Soc. A, 373, no. 2050, 20140278 (2015).

  30. Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations, with A. Castro and D. Córdoba.
    Duke Mathematical Journal, 165, no. 5, 935-984 (2016).

  31. Structural stability for the splash singularities of the water waves problem, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.
    Discrete and Continuous Dynamical Systems – A, 34, no. 12, 4997-5043 (2014).

  32. Remarks on geometric properties of SQG sharp fronts and $\alpha$ patches, with A. Castro, D. Córdoba and A. M. Zamora.
    Discrete and Continuous Dynamical Systems – A, 34, no. 12, 5045-5059 (2014).

  33. On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof, with R. Granero-Belinchón.
    Nonlinearity, 27, no. 6, 1471-1498 (2014).

  34. Finite time singularities for water waves with surface tension, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.
    J. Math. Phys., 53, no. 11, 115622 (2012). Special Issue “Incompressible Fluids, Turbulence and Mixing”.

  35. Finite time singularities for the free boundary incompressible Euler equations, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.
    Annals of Mathematics, 178, no. 3, 1061-1134 (2013).

  36. Splash singularity for water waves, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.
    Proc. Natl. Acad. Sci., 109, no. 3, 733-738 (2012).

  37. The Bounded Confidence Model Of Opinion Dynamics, with C. Graham and J.-Y. Le Boudec.
    Math. Mod. Meth. Appl. Sci. 22, num. 2, 1150007(1-46), (2012).

  38. Comment on “Mixing beliefs among interacting agents”,
    with J.-Y. Le Boudec.
    Adv. Complex Syst., 15, no. 7, 1250028(1-7), (2012).