Skip to main content

Ángel Castro

Institution: CSIC

Position: Científico Titular

Phone: +34 912999 783


Personal Webpage


Biographical Review

Angel Castro is a researcher in the Universidad Autónoma de Madrid and also a member of the ICMAT. His research interests lie in fluid mechanics. Currently his work is focus on interface problems like Water Waves and the Muskat problem.

Research Interests

Partial differential equations and fluid mechanics



? 1. " Global existence, singularities and Ill-posedness for a non-local flux" (with D. Córdoba),  Advances in Math. 219 (2008), 6, 1916-1936.

2. "Self-similar solutions for a transport equation with non-local  flux"  (with D. Córdoba), Chinese Annals of Math. Series B. 30 (2009), 5, 505-512.

3.  "Incompressible flow in porous media with fractional diff usion" (with D. Córdoba, F.Gancedo & R. Orive) Nonlinearity 22 (2009), 8, 1791-1815.

4. "Infi nite energy solutions of the surface quasi-geostrophic equation." (with D. Córdoba), Advances in Math. 225 (2010) 18201829.

5.  "Singularity formations for a surface wave model" (with D. Córdoba & F. Gancedo), Nonlinearity 11 (2010) 2835-2849.

 6. "Some recent results on the Muskat problem" (with D. Córdoba & F. Gancedo), Proceedings of Journees Equations aux Derivees Partielles (Port d'Albret, 2010).

 7. "Turning waves and breakdown for incompressible flows" (with D. Cordoba, C. Fefferman, F. Gancedo & M. López-Fernández), Proceedings of the National Academy of Sciences, 108 (12) (2011) 4754-4759.

8. "Rayleigh- Taylor breakdown for the Muskat problem with applications to water waves" (with D. Córdoba, C. Feff erman, F. Gancedo & M. López-Fernández), Ann.of Math. 175 (2012) 909-948.

 9. "Splash singularity for water waves" (with D. Córdoba, C. Feff erman, F. Gancedo and J. Gómez-Serrano), Proc. Natl. Acad. Sci., 109, no. 3, 733-738 (2012)

 10. "Finite time singularities for water waves with surface tension" (with D. Córdoba, C.Feff erman, F. Gancedo and J. Gómez-Serrano).  J. Math. Phys. 53, 115622 (2012) 

 11.  "A Naive Parametrization for the Vortex-Sheet problem", (with D. Córdoba  &  F. Gancedo).? ?Mathematical aspects on fluid Mechanics. London Math. Soc. Lecture Note Ser.pp. 88 -115.Cambridge University Press,2012. 

 12. "Finite time singularities for the free boundary incompressible Euler equations", (with D. Córdoba, C. Feff erman, F. Gancedo and J. Gómez-Serrano).   Annals of Math, 178, no. 3, 1061-1134 (2013).

13. "Breakdown of smoothness of the Muskat problem" (with D. Córdoba, C. Feff erman & F. Gancedo). Arch. Ration. Mech. Anal., 208, no. 3, 805-909 (2013). (2013).

 14. "Structural Stability for the splash singularities of the water waves problem" (with D. Córdoba, C. Fefferman, F. Gancedo & J. Gómez-Serrano). Discrete Continuos Dynamical Systems 34 (12), 4997-5043 (2014).

15. "Remarks on the geometric properties of the SQG sharp fonts and $\alpha$-patches$. (with D. Córdoba, J. Gómez-Serrano & A. Martin-Zamora). Discrete Continuos Dynamical System 34 (12), 5045-5059, (2014).

16. "Splash singularities for the one-phase Muskat problem in stables regimes " (with D. Córdoba, C. Fefferman & F. Gancedo). To appear in Arch. Ration. Mech. Anal.

17. "Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water wave problem with vorticity" (with David Lannes). Indiana Univ. Math. J. 64 (2015) 1169--1270

18. "Horizontal vorticity generation for fully nonlinear shallow water model" (with David Lannes). J. Fluid Mech. 759 (2014), 642--675.

19." Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations" (with D. Córdoba and J. Gómez-Serrano)   To appear in DUKE Math Journal.

20. "Uniformly rotating analytic global patch solutions for active scalars "(with D. Córdoba and J. Gómez-Serrano)  To appear in Annals of PDE (2016)


1. " Splash singularities for the free boundary Navier-Stokes equations"(with D. Córdoba, C. Fefferman, F. Gancedo & J. Gómez-Serrano)   Preprint arxiv:1504.02775.

2."Mixing solutions for the Muskat problem " (with D. Córdoba and D. Faraco).

3."Global smooth solutions for the inviscid SQG equation " (with D. Córdoba and J. Gómez-Serrano ) Preprint arxiv:1603.03325.