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Diego C├│rdoba

Institution: Consejo Superior de Investigaciones Científicas

Position: Profesor de Investigación

Office: 418          Phone:+34 912999 798

E-mail: dcg()icmat.es

Short CV

Personal Webpage

 

Biographical Review

Diego Córdoba is a Professor at the Instituto de Ciencias Matemáticas (ICMat-CSIC) and the Scientific Director of the Severo Ochoa program 2016-2019. 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 50 research papers, including articles in Annals of Mathematics, Journal of the American Mathematical Society, Communications on Pure and Applied Mathematics, Duke Math. Journal, 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 also been selected as an invited Speaker at the next International Congress of Mathematicians (ICM) in Rio de Janeiro, Brasil (2018).

Research Interest

 Partial Differential Equations and Fluid Mechanics

Publications

Paper to appear

  1. "Mixing solutions for the Muskat problem" (with A. Castro & D. Faraco). Preprint arxiv:1605:04822
  2. "Splash singularities for the free boundary Navier-Stokes equations" (with A. Castro, C. Fefferman, F. Gancedo, J. G├│mez-Serrano), Preprint arxiv:1504.02775.
  3. "Uniqueness for SQG patch solutions" (with A. C├│rdoba & F. Gancedo). Preprint arxiv: 1605.06663
  4. "Uniformly rotating smooth solutions for the incompressible 2D Euler equations" (with A. Castro & J. G├│mez-Serrano). Preprint arxiv: 1612.08964
  5. "Global solutions for the generalized SQG patch equation" (with J. G├│mez-Serrano & A. D. Ionescu). Preprint arxiv: 1705.10842

 

 

Publications (Research papers in the last 10 years)

  1. "Global smooth solutions for the inviscid SQG equation" (with A. Castro & J. G├│mez-Serrano). Preprint arxiv:1603.03325. To appear in Mem. Amer. Math. Soc.
  2. "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.
  3. “Non-splat singularity for the one-phase Muskat problem” (with T. Pernas), Trans. Amer. Math. Soc. Vol. 369, no.1, (2017), 711-754.
  4. "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).
  5. "Uniformly rotating analytic global patch solutions for active scalars" (with A. Castro & J. G├│mez-Serrano), Annals of PDE 2 (2016), no.1, Art 1, 34pp.
  6. "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.
  7. “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.
  8. "Splash and almost-Splash stationary solutions to the Euler equations" (with A. Enciso & N. Grubic). Advances in Math. 288(2016) 922-941.
  9. "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.
  10. "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).
  11. "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).
  12. "The confined Muskat problem: differences with the deep water regime" (with R. Granero and R. Orive).  Comm. Math. Sci. 12 (3), 423-455 (2014).
  13. "Local solvability and turning for the inhomogeneous Muskat problem" (with  L. Berselli & R. Granero ).  Interfaces and Free Boundaries 16, (2) 175-213 (2014).
  14. "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).
  15. "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).
  16. "Porous media: the Muskat problem in 3D " (with A. Cordoba & F. Gancedo ), Analysis & PDE., 6, no. 2, 447497 (2013).
  17. “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).
  18. "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). 
  19. "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). 
  20. "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). 
  21. “Finite time singularities of water waves with surface tension” (with A. Castro, C. Fefferman, F. Gancedo & J. Gómez-Serrano). J. Math. Phys. 53 (2012).       
  22. “ 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. 
  23. “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.
  24. “Interface evolution: the Hele-Shaw and Muskat problems” (with A. Córdoba and F. Gancedo), Annals of Math. 173 (2011), (1), 477-544.
  25.  “Singularity formations for a surface wave model” (with A. Castro & F. Gancedo.) Nonlinearity 11 (2010) 2835-2849.
  26.  “Infinite energy solutions of the surface quasi-geostrophic equation.” (with A. Castro.) Advances in Math. 225 (2010) 18201829.
  27.  “Absence of squirt singularities for the multi-phase Muskat problem.” (with F. Gancedo.) Comm. Math. Phys. 299 (2010), 2, 561-575.
  28.  “Interface evolution: water waves in 2-D” (with A. Córdoba & F. Gancedo ), Advances in Math. 223 (2010), 1, 120-173.
  29.  “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.
  30. “ 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.
  31.  “ Incompressible flow in porous media with fractional diffusion” (with A. Castro, F. Gancedo & R. Orive) Nonlinearity 22 (2009), 8, 1791-1815.
  32. “ 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.
  33.  “ A maximum principle for the Muskat problem with different densities” (with F. Gancedo ) Comm. Math. Phys. 286 (2009), 2, 681-696.
  34. “Global existence, singularities and Ill-possednes for a non-local flux” (with A. Castro), Advances in Math. 219 (2008), 6, 1916-1936. 
  35. “A note on the interface dynamics for convection in porous media” (with F. Gancedo & R. Orive), Physica D 237 (2008), 1488-1497.