Research

My research interests lie within analysis, partial differential equations and fluid mechanics. More specifically, I am interested in the evolution of moving incompressible fluid interfaces coming from physical models.
During my graduate career, I have studied the global well-posedness and interface regularity for patch problems in nonlinear parabolic equations such as Navier-Stokes and Boussinesq. I have also worked on the Muskat problem, addressing additional questions like large-time decay of solutions or ill-posedness.

A brief summary of my current research can be found in this short version of my ResearchStatement. I am always avalaible through email for more information (eduardogarcia@us.es).

Publications:

  1. Global regularity for 2D Boussinesq temperature patches with no diffusion,
    with F. Gancedo. Ann. PDE (2017), 3: 14.
  2. Global regularity of 2D density patches for inhomogeneous Navier-Stokes,
    with F. Gancedo. Arch. Ration. Mech. Anal. (2018).
  3. On the Muskat problem with viscosity jump: Global in time results,
    with F. Gancedo, N. Patel and R. Strain.  Submitted, arXiv:1710.11604, (2017).

Preprints of my papers can be found in ArXiv, ResearchGate. Information about talks, workshops and grants can be found in my Curriculum Vitae.