Institution: Consejo Superior de Investigaciones Científicas
Position: Profesor de Investigación
Office: 418 Phone:+34 912999 798
Email: dcg()icmat.es
Biographical Review
Diego Córdoba is a Professor at the Instituto de Ciencias Matemáticas (ICMatCSIC) and the Scientific Director of the Severo Ochoa program 20162019. 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 60 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 (19971998), 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 (20082013). 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).
Recently, Diego has been awarded an ERC Advanced Grant (20182023).
Research Interest
Partial Differential Equations and Fluid Mechanics
Publications
Paper to appear
 "Mixing solutions for the Muskat problem" (with A. Castro & D. Faraco). Preprint arxiv:1605:04822
 "Splash singularities for the free boundary NavierStokes equations" (with A. Castro, C. Fefferman, F. Gancedo, J. GÃ³mezSerrano), Preprint arxiv:1504.02775.
 "Global solutions for the generalized SQG patch equation" (with J. GÃ³mezSerrano & A. D. Ionescu). Preprint arxiv: 1705.10842
 "Global wellposedness for the 2D stable Muskat problem in H^{3/2} " (with O. Lazar).Preprint arxiv:1803.07528.
 "On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term" (with A. Castro & D. Lear). Preprint arXiv:1805.05179
Publications (Research papers in the last 10 years)
 "Global existence of quasistratified solutions for the confined IPM equation" (with A. Castro & D. Lear). Preprint arxiv:1804.08490. To appear in Arch. Ration. Mech. Anal.
 "Uniformly rotating smooth solutions for the incompressible 2D Euler equations" (with A. Castro & J. GÃ³mezSerrano). Preprint arxiv: 1612.08964. To appear in Arch. Ration. Mech. Anal.
 "Global smooth solutions for the inviscid SQG equation" (with A. Castro & J. GÃ³mezSerrano). Preprint arxiv:1603.03325. To appear in Mem. Amer. Math. Soc.
 "Uniqueness for SQG patch solutions" (with A. CÃ³rdoba & F. Gancedo) Trans. Amer. Math. Soc. Ser. B 5 (2018), 131.
 "On the splash and splat singularities for the onephase inhomogeneous Muskat Problem" (with T. Pernas) To appear in Journal Nonlinear Sci. https://doi.org/10.1007/s003320179418x
 "A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable" (with J. GÃ³mezSerrano & A. ZlatoÅ¡). Anal. PDE 10 (2017), no 2, 367378.

“Nonsplat singularity for the onephase Muskat problem” (with T. Pernas), Trans. Amer. Math. Soc. Vol. 369, no.1, (2017), 711754.
 "On the Muskat problem: global in time results in 2D and 3D" (with P. Constantin, F. Gancedo, Luis RodriguezPiazza & R. Strain), Amer. J. Math. Vol 138, no.6, (2016).
 "Uniformly rotating analytic global patch solutions for active scalars" (with A. Castro & J. GÃ³mezSerrano), Annals of PDE 2 (2016), no.1, Art 1, 34pp.
 "Splash singularities for the onephase Muskat problem in stable regimes" (with A. Castro, C. Fefferman & F. Gancedo), Arch. Ration. Mech. Anal. Vol, 222, no.1, (2016), 213243.

“Existence and regularity of rotating global solutions for the generalized surface quasigeostrophic equations” (with A. Castro & J. GómezSerrano). Duke Math Journal. Vol 165, no.5, (2016), 935984.

"Splash and almostSplash stationary solutions to the Euler equations" (with A. Enciso & N. Grubic). Advances in Math. 288(2016) 922941.

"A note in stability shifting for the Muskat problem" (with J. GómezSerrano & A. Zlatos). Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 373 (2015) no.2050, 20140278,10pp.
 "Remarks on geometric properties of the SQG sharp front and the alphapatches" (with A. Castro, J. GomezSerrano and A. Martin). Discrete Continuos Dynamical System 34 (12), 50455059, (2014).
 "Structural stability for the splash singularities of the water wave problem" (with A. Castro, C. Fefferman, F. Gancedo and J. GomezSerrano). Discrete Continuos Dynamical Systems 34 (12), 49975043 (2014).
 "The confined Muskat problem: differences with the deep water regime" (with R. Granero and R. Orive). Comm. Math. Sci. 12 (3), 423455 (2014).
 "Local solvability and turning for the inhomogeneous Muskat problem" (with L. Berselli & R. Granero ). Interfaces and Free Boundaries 16, (2) 175213 (2014).
 "Finite time singularities for the free boundary incompressible Euler equations" (with A. Castro, C. Fefferman, F. Gancedo & J. GomezSerrano), Annals of Math, 178, no. 3, 10611134 (2013).
 "Breakdown of smoothness for the Muskat problem" (with A. Castro, C. Fefferman & F. Gancedo ), Arch. Ration. Mech. Anal., 208, no. 3, 805909 (2013).
 "Porous media: the Muskat problem in 3D " (with A. Cordoba & F. Gancedo ), Analysis & PDE., 6, no. 2, 447497 (2013).
 “On the global existence for the Muskat problem” (with P. Constantin, F. Gancedo and R. Strain), J. Eur. Math. Soc. (JEMS) 15, 201227 (2013).
 "Splash singularities for water waves". (with A. Castro, C. Fefferman, F. Gancedo and J. GómezSerrano) Proc. Natl. Acad. Sci. 109 (3):733738 (2012).
 "RayleighTaylor breakdown for the Muskat problem with applications to water waves". (with A. Castro, Ch. Fefferman, F.Gancedo and M. LópezFernández) Annals of Math. 175 (2): 909948 (2012).
 "Generalized surface quasigeostrophic equations with singular velocities". ( with D. Chae, P. Constantin, F. Gancedo and J. Wu) Comm. Pure Applied Math. 65 (8): 10371066 (2012).
 “Finite time singularities of water waves with surface tension” (with A. Castro, C. Fefferman, F. Gancedo & J. GómezSerrano). J. Math. Phys. 53 (2012).
 “ Lack of uniqueness for weak solutions of the incompressible porous media equation. (with D. Faraco and F. Gancedo) Arch. Rat. Mech. Anal. 20 (2011), 725746.
 “Turning waves and breakdown for incompressible flows” (with A. Castro, C. Fefferman, F. Gancedo and M. López), Proc. Natl. Acad. Sci. 108 (2011), 12, 47544759.
 “Interface evolution: the HeleShaw and Muskat problems” (with A. Córdoba and F. Gancedo), Annals of Math. 173 (2011), (1), 477544.
 “Singularity formations for a surface wave model” (with A. Castro & F. Gancedo.) Nonlinearity 11 (2010) 28352849.
 “Infinite energy solutions of the surface quasigeostrophic equation.” (with A. Castro.) Advances in Math. 225 (2010) 18201829.
 “Absence of squirt singularities for the multiphase Muskat problem.” (with F. Gancedo.) Comm. Math. Phys. 299 (2010), 2, 561575.
 “Interface evolution: water waves in 2D” (with A. Córdoba & F. Gancedo ), Advances in Math. 223 (2010), 1, 120173.
 “On the regularity of the solutions to the 3D NavierStokes equations: a remark on the role of the helicity” (with Luigi C. Berselli), Comptes Rendus Mathematique 347 (2009), 613618.
 “ Selfsimilar solutions for a transport equation with nonlocal flux” (with A. Castro) Chinese Annals of Math. Series B. 30 (2009), 5, 505512.
 “ Incompressible flow in porous media with fractional diffusion” (with A. Castro, F. Gancedo & R. Orive) Nonlinearity 22 (2009), 8, 17911815.
 “ The RayleighTaylor condition for the evolution of irrotational fluid interfaces” (with A. Córdoba & F. Gancedo ), Proc. Natl. Acad. Sci. 106 (2009), 27, 1095510959.
 “ A maximum principle for the Muskat problem with different densities” (with F. Gancedo ) Comm. Math. Phys. 286 (2009), 2, 681696.
 “Global existence, singularities and Illpossednes for a nonlocal flux” (with A. Castro), Advances in Math. 219 (2008), 6, 19161936.
 “A note on the interface dynamics for convection in porous media” (with F. Gancedo & R. Orive), Physica D 237 (2008), 14881497.