Preprints

Time periodic solutions for 2D Euler near Taylor-Couette flow

    arXiv:2311.06885 (2023)

    Authors: Á. Castro, D. Lear

Entropy solutions to macroscopic IPM

    arXiv:2309.03637 (2023)

    Authors: Á. Castro, D. Faraco, B. Gebhard

Research papers

Stability of traveling waves for the Burgers-Hilbert equation

    APDE (2023)

    Authors: Á. Castro, D. Córdoba, F. Zheng

Traveling waves near Couette flow for the 2D Euler equation

     Comm. Math. Phys. (2023)

    Authors: Á. Castro, D. Lear

Localized mixing zone for Muskat bubbles and turned interfaces

    Ann. PDE (2022)

    Authors: Á. Castro, D. Faraco, F. Mengual

Mixing solutions for the Muskat problem

    Invent. Math. (2021)

    Authors: Á. Castro, D. Córdoba, D. Faraco

The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation

    Ann. I. H. Poincare-An. (2021)

    Authors: Á. Castro, D. Córdoba, F. Zheng

Semiclassical estimates for pseudodifferential operators and the Muskat problem in the unstable regime

    Comm. Partial Differential Equations (2021)

    Authors: V. Arnaiz, Á. Castro, D. Faraco

Singularity formation for the fractional Euler-alignment system in 1D

    Trans. Amer. Math. 374 (2021)

    Authors: V. Arnaiz, Á. Castro

Global solutions for the inviscid SQG equation

    Mem. Amer. Math. Soc. 266 (2020)

    Authors: Á. Castro, D. Córdoba, J. Gómez-Serrano

Degraded mixing solutions for the Muskat problem

    Calc. Var. Partial Differential Equations 58 (2019)

    Authors: Á. Castro, D. Córdoba, J. Gómez-Serrano

On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term

    Math. Models Methods Appl. Sci. 29 (2019), 189-203.

    Authors: Á. Castro, D. Córboba, D. Lear

Global existence of quasi-stratified solutions for the confined IPM equation

    Arch. Ration. Mech. Anal. 232 (2019)

    Authors: Á. Castro, D. Córdoba, D. Lear

Splash singularities for the free boundary Navier-Stokes equations

    Ann. PDE 5 (2019)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, J. Gómez-Serrano

Uniformly rotating smooth solutions for the incompressible 2D Euler equations

    Arch. Ration. Mech. Anal. 231 (2019)

    Authors: Á. Castro, D. Córdoba, J. Gómez-Serrano

Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations

    Duke Math. J. 165 (2016)

    Authors: Á. Castro, D. Córdoba, J. Gómez-Serrano

Uniformly rotating analytic global patch solutions for active scalars

    Ann. PDE 2 (2016)

    Authors: Á. Castro, D. Córdoba, J. Gómez-Serrano

Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves problem con vorticity

    Indiana Univ. Math. J. 65 (2015)

    Authors: Á. Castro, D. Lannes

Fully nonlinear long-wave models in the presence of vorticity

    Indiana Univ. Math. J. 759 (2014)

    Authors: Á. Castro, D. Lannes

Remarks on the geometric properties of the SQG sharp fronts and alpha-patches

    DCDS-A 34 (2014)

    Authors: Á. Castro, D. Córdoba, J. Gómez-Serrano, A. Zamora

Structural stability for the splash singularities of the water waves problem

    DCDS-A 34 (2014)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, J. Gómez-Serrano

Breakdown of smoothness of the Muskat problem

    Arch. Ration. Mech. Anal. 208 (2013)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo

Finite time singularities for the free boundary incompressible Euler equations

    Ann. of Math. 178 (2013)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, J. Gómez-Serrano

A naive parametrization for the Vortex-Sheet problem

    London Math. Soc. Lecture Note Ser. (2012)

    Authors: Á. Castro, D. Córdoba, F. Gancedo

Finite time singularities for water waves con surface tension

    J. Math. Phys. (2012)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, J. Gómez-Serrano

Splash singularity for water waves

    Proc. Natl. Acad. Sci. 109 (2012)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, J. Gómez-Serrano

Rayleigh- Taylor breakdown for the Muskat problem with applications to water waves

    Ann. of Math. 175 (2012)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, M. López-Fernández

Turning waves and breakdown for incompressible ows

    Proc. Natl. Acad. Sci. 108 (2011)

    Authors: Á. Castro, D. Córdoba, C. Fefferman, F. Gancedo, M. López-Fernández

Singularity formations for a surface wave model

    Nonlinearity 11 (2010)

    Authors: Á. Castro, D. Córdoba, F. Gancedo

Infinite energy solutions of the surface quasi-geostrophic equation

    Adv. Math. 225 (2010)

    Authors: Á. Castro, D. Córdoba

Incompressible flow in porous media con fractional diffusion

    Nonlinearity 22 (2009)

    Authors: Á. Castro, D. Córdoba, F. Gancedo, R. Orive

Self-similar solutions for a transport equation with non-local flux

    Chinese Ann. Math. Ser. B 30 (2009)

    Authors: Á. Castro, D. Córdoba

Global existence, singularities and Ill-posedness for a non-local flux

    Adv. Math. 219 (2008)

    Authors: Á. Castro, D. Córdoba

Proceedings

Mixing solutions for IPM

    Journées Équations aux dérivées partielles (2017)

    Authors: Á. Castro

Some recent results for the Muskat problem

    Journées Équations aux dérivées partielles (2010)

    Authors: Á. Castro, D. Córdoba, F. Gancedo