**Institution: **CSIC

**Position: **CientÃfico Titular

**Phone: **+34 912999 783

**Email: **angel_castro@icmat.es

#### 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

www.icmat.es/events/seminar/pizza

#### Publications

? 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 diffusion" (with D. Córdoba, F.Gancedo & R. Orive) Nonlinearity 22 (2009), 8, 1791-1815.

4. "Infinite 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. Fefferman, F. Gancedo & M. López-Fernández), Ann.of Math. 175 (2012) 909-948.

9. "Splash singularity for water waves" (with D. Córdoba, C. Fefferman, 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.Fefferman, 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. Fefferman, F. Gancedo and J. Gómez-Serrano). Annals of Math, 178, no. 3, 1061-1134 (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)

**PAPERS TO APPEAR **

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.