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Diego Córdoba Gazolaz

Institution: CSIC

Position: Profesor de Investigación

Office: 418

Phone: +34 912999 798

Email: dcg@icmat.es


About:

Short CV

Diego Córdoba is a Professor at the Instituto de Ciencias Matemáticas (ICMat-CSIC) and the Scientific Director of the Severo Ochoa program 2016-2019 and 2020-2023. He obtained his PhD in Mathematics from Princeton University in 1998. He has held full time academic positions at the Institute for Advanced Study in Princeton (Member), University of Chicago (L. E. Dickson Instructor) and Princeton University (Assistant Professor ).

His research interest is focused on Partial Differential Equations, Analysis and Fluid Mechanics. He has coauthored over 80 research papers, including articles in Annals of Mathematics, Journal of the American Mathematical Society, Inventiones Math., Communications on Pure and Applied Mathematics, Duke Math. Journal, Memoirs of the AMS, Ann. Sci. Ec. Norm. Sup., Communications in Mathematical Physics, Archives Rational Mechanics and Analysis, Journal of the European Mathematical Society and the Proceedings of the National Academy of Sciences USA.

Diego has been awarded an Alfred P. Sloan Doctoral Dissertation Fellowship (1997-1998), American Institute of Mathematics Postdoctoral Fellowship in 1999, Ramón y Cajal Researcher position in 2002, the SEMA Prize (Sociedad Española de Matemática Aplicada) for young researchers in 2005, and the Miguel Catalán Young Award 2011 from the Comunidad Autónoma de Madrid. In 2008 he obtained a Starting Independent Research Grant from the European Research Council (2008-2013). He was a Minerva Distinguished Visitor at the Math. Department of Princeton University from September 2014 until February 2015. He has been a member of the Institute for Advanced Study (IAS) in Princeton during the spring 2022.

He has also been selected as an invited Speaker at the International Congress of Mathematicians (ICM) in Rio de Janeiro, Brazil (2018) and has been awarded an ERC (European Research Council) Advanced Grant (2018-2023).

Recently, Diego has just received the 2022 Margarita Salas Medal Award for research supervision from the Spanish National Research Council (CSIC) and has been awarded the 2023 'Julio Rey Pastor' National Research Prize in the field of Mathematics and Information and Communication Technologies.

 

Research Interests

Partial Differential Equations and Fluid Mechanics

 

Publications

Paper to appear

  1. "Blow-up for the incompressible 3D-Euler equations with uniform $C^{1, 1/2-epsilon}cup L^2$ force (with L. Martinez-Zoroa) Preprint arxiv:2309.08495.
  2. "Finite time singularities to the 3D incompressible Euler equations for solutions in $C^{infty}(mathbb{R}^3 setminus {0})cap C^{1,alpha}cap L^2$" (with L. Martinez-Zoroa & F. Zheng) Preprint arxiv:2308.12197.
  3. "Global unique solutions with instantaneous loss of regularity for SQG with fractional diffusion" (with Luis Martínez-Zoroa). Preprint arXiv: 2303.07178.
  4. "Finite-time singularity formation for angled-crested water waves" (with Alberto Enciso & Nastasia Grubic) Preprint arXiv:2303.00027.
  5. "Non-existence and strong ill-posedness in $C^{k,β}$ for the generalized Surface Quasi-geostrophic equation" (with Luis Martínez-Zoroa). Preprint arXiv:2207.14385.

Publications (Research papers in the last 15 years)

  1. "Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations" (with Luis Martínez-Zoroa & Wojciech Ozanski). Preprint arXiv:2210.17458. To appear in Duke Math Journal.
  2. "Stability of traveling waves for the Burgers-Hilbert equation" (with A. Castro & F. Zheng) Anal. PDE 16 (2023), no. 9, 2109–2145.
  3. "Local wellposedness for the free boundary incompressible Euler equations with interfaces that exhibit cusps and corners of nonconstant angle" (with Alberto Enciso & Nastasia Grubic). Advances in Math. 433, 2023, 109299.
  4. "Non existence and strong ill-posedness in $C^k$ and Sobolev spaces for SQG" (with Luis Martínez-Zoroa). Adv. Math. 407 (2022), Paper No. 108570.
  5. "Global well-posedness for the 2D stable Muskat problem in $H^{3/2} " (with O. Lazar). Annales Scientifiques de l'École Normale Supérieure. (4) 54 (2021), no. 5, 1315–1351.
  6. "Mixing solutions for the Muskat problem" (with A. Castro & D. Faraco). Inventiones Mathematicae, 2021, 226(1), pp. 251–348.
  7. "The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation". (with A. Castro & F. Zheng) Ann. Inst. H. Poincaré Anal. Non Linéaire, 2021, 38(5), pp. 1583–1603.
  8. "Self-intersecting interfaces for stationary solutions of the two-fluid Euler equations" (with A. Enciso & N. Grubic). Annals of PDE. Annals of PDE, 2021, 7(1), 12.
  9. "Global smooth solutions for the inviscid SQG equation" (with A. Castro & J. Gómez-Serrano). Mem. Amer. Math. Soc. 266 (2020), no.1292, v+89 pp.
  10. "On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term" (with A. Castro & D. Lear). Math. Models Methods Appl. Sci. 29 (2019), no. 7, 1227–1277.
  11. "Global solutions for the generalized SQG patch equation" (with J. Gómez-Serrano & A. D. Ionescu). Arch. Ration. Mech. Anal. 233 (2019) no3. 1211-1251.
  12. "Splash singularities for the free boundary Navier-Stokes equations" (with A. Castro, C. Fefferman, F. Gancedo, J. Gómez-Serrano), Ann. PDE 5 (2019), no.1, Art.12, 117pp.
  13. "Global existence of quasi-stratified solutions for the confined IPM equation" (with A. Castro & D. Lear). Arch. Ration. Mech. Anal, 232 (2019), no.1, 437-471.
  14. "Uniformly rotating smooth solutions for the incompressible 2D Euler equations" (with A. Castro & J. Gómez-Serrano). Arch. Ration. Mech. Anal., 231(2019), no.2, 719-785.
  15. "Uniqueness for SQG patch solutions" (with A. Córdoba & F. Gancedo) Trans. Amer. Math. Soc. Ser. B 5 (2018), 1-31.
  16. "On the splash and splat singularities for the one-phase inhomogeneous Muskat Problem" (with T. Pernas) Journal Nonlinear Sci., 28(2018), no.6, 2077-2126
  17. "A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable" (with J. Gómez-Serrano & A. Zlatoš). Anal. PDE 10 (2017), no 2, 367378.
  18. "Non-splat singularity for the one-phase Muskat problem” (with T. Pernas), Trans. Amer. Math. Soc. Vol. 369, no.1, (2017), 711-754.
  19. "On the Muskat problem: global in time results in 2D and 3D" (with P. Constantin, F. Gancedo, Luis Rodriguez-Piazza & R. Strain), Amer. J. Math. Vol 138, no.6, (2016).
  20. "Uniformly rotating analytic global patch solutions for active scalars" (with A. Castro & J. Gómez-Serrano), Annals of PDE 2 (2016), no.1, Art 1, 34pp.
  21. "Splash singularities for the one-phase Muskat problem in stable regimes" (with A. Castro, C. Fefferman & F. Gancedo), Arch. Ration. Mech. Anal. Vol, 222, no.1, (2016), 213-243.
  22. “Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations” (with A. Castro & J. Gómez-Serrano). Duke Math Journal. Vol 165, no.5, (2016), 935-984.
  23. "Splash and almost-Splash stationary solutions to the Euler equations" (with A. Enciso & N. Grubic). Advances in Math. 288(2016) 922-941.
  24. "A note in stability shifting for the Muskat problem" (with J. Gómez-Serrano & A. Zlatos). Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 373 (2015) no.2050, 20140278,10pp.
  25. "Remarks on geometric properties of the SQG sharp front and the alpha-patches" (with A. Castro, J. Gomez-Serrano and A. Martin).Discrete Continuos Dynamical System 34 (12), 5045-5059, (2014).
  26. "Structural stability for the splash singularities of the water wave problem" (with A. Castro, C. Fefferman, F. Gancedo and J. Gomez-Serrano). Discrete Continuos Dynamical Systems 34 (12), 4997-5043 (2014).
  27. "The confined Muskat problem: differences with the deep water regime" (with R. Granero and R. Orive). Comm. Math. Sci. 12 (3), 423-455 (2014).
  28. "Local solvability and turning for the inhomogeneous Muskat problem" (with L. Berselli & R. Granero ). Interfaces and Free Boundaries 16, (2) 175-213 (2014).
  29. "Finite time singularities for the free boundary incompressible Euler equations" (with A. Castro, C. Fe fferman, F. Gancedo & J. Gomez-Serrano), Annals of Math, 178, no. 3, 1061-1134 (2013).
  30. "Breakdown of smoothness for the Muskat problem" (with A. Castro, C. Fe fferman & F. Gancedo ), Arch. Ration. Mech. Anal., 208, no. 3, 805-909 (2013).
  31. "Porous media: the Muskat problem in 3D " (with A. Cordoba & F. Gancedo ), Analysis & PDE., 6, no. 2, 447497 (2013).
  32. “On the global existence for the Muskat problem” (with P. Constantin, F. Gancedo and R. Strain), J. Eur. Math. Soc. (JEMS) 15, 201-227 (2013).
  33. "Splash singularities for water waves". (with A. Castro, C. Fefferman, F. Gancedo and J. Gómez-Serrano) Proc. Natl. Acad. Sci. 109 (3):733-738 (2012).
  34. "Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves". (with A. Castro, Ch. Fefferman, F.Gancedo and M. López-Fernández) Annals of Math. 175 (2): 909-948 (2012).
  35. "Generalized surface quasi-geostrophic equations with singular velocities". ( with D. Chae, P. Constantin, F. Gancedo and J. Wu) Comm. Pure Applied Math. 65 (8): 1037-1066 (2012).
  36. “Finite time singularities of water waves with surface tension” (with A. Castro, C. Fefferman, F. Gancedo & J. Gómez-Serrano). J. Math. Phys. 53 (2012).
  37. “ Lack of uniqueness for weak solutions of the incompressible porous media equation. (with D. Faraco and F. Gancedo) Arch. Rat. Mech. Anal. 20 (2011), 725-746.
  38. “Turning waves and breakdown for incompressible flows” (with A. Castro, C. Fefferman, F. Gancedo and M. López), Proc. Natl. Acad. Sci. 108 (2011), 12, 4754-4759.
  39. “Interface evolution: the Hele-Shaw and Muskat problems” (with A. Córdoba and F. Gancedo), Annals of Math. 173 (2011), (1), 477-544.
  40. “Singularity formations for a surface wave model” (with A. Castro & F. Gancedo.) Nonlinearity 11 (2010) 2835-2849.
  41. “Infinite energy solutions of the surface quasi-geostrophic equation.” (with A. Castro.) Advances in Math. 225 (2010) 18201829.
  42. “Absence of squirt singularities for the multi-phase Muskat problem.” (with F. Gancedo.) Comm. Math. Phys. 299 (2010), 2, 561-575.
  43. “Interface evolution: water waves in 2-D” (with A. Córdoba & F. Gancedo ), Advances in Math. 223 (2010), 1, 120-173.
  44. “On the regularity of the solutions to the 3D Navier-Stokes equations: a remark on the role of the helicity” (with Luigi C. Berselli), Comptes Rendus Mathematique 347 (2009), 613-618.
  45. “ Self-similar solutions for a transport equation with non-local flux” (with A. Castro) Chinese Annals of Math. Series B. 30 (2009), 5, 505-512.
  46. “ Incompressible flow in porous media with fractional diffusion” (with A. Castro, F. Gancedo & R. Orive) Nonlinearity 22 (2009), 8, 1791-1815.
  47. “ The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces” (with A. Córdoba & F. Gancedo ), Proc. Natl. Acad. Sci. 106 (2009), 27, 10955-10959.
  48. “ A maximum principle for the Muskat problem with different densities” (with F. Gancedo ) Comm. Math. Phys. 286 (2009), 2, 681-696.
  49. “Global existence, singularities and Ill-possednes for a non-local flux” (with A. Castro), Advances in Math. 219 (2008), 6, 1916-1936.
  50. “A note on the interface dynamics for convection in porous media” (with F. Gancedo & R. Orive), Physica D 237 (2008), 1488-1497.