Research

My research interests lie within analysis, partial differential equations and fluid mechanics. More specifically, I am interested in the evolution of moving interfaces in incompressible flows coming from physical models. Since September, 2021, I work on the MSCA-IF-2020 project CAMINFLOW.

Publications:

  1. Global Regularity of 2D N-S Free Boundary with Small Viscosity Contrast, with F. Gancedo. Preprint, arXiv:2109.08764, (2021).
  2. Quantitative Hölder Estimates for Even Singular Integral Operators on Patches, with F. Gancedo. Preprint, arXiv:2109.08762, (2021).
  3. Self-similar solutions for the Muskat equation, with J. Gómez-Serrano, H. Q. Nguyen, B. Pausader. Preprint, arXiv:2109.02565, (2021).
  4. The Peskin Problem with Viscosity Contrast, with Y. Mori, R. Strain. Accepted in Analysis & PDE, arXiv:2009.03360, (2020). (Link to ArXiv)
  5. Global Regularity for Gravity Unstable Muskat Bubbles, with F. Gancedo, N. Patel and R. Strain. Accepted in Memoirs of the AMS, arXiv:1902.02318, (2019). (Link to ArXiv)
  6. Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo.  Communications in Mathematical Physics, 376, 1705-1736 (2020). (Link to ArXiv)
  7. On the Muskat problem with viscosity jump: Global in time results,
    with F. Gancedo, N. Patel and R. Strain. Advances in Mathematics, 345,  552-597, (2019). (Link to ArXiv)
  8. Global regularity of 2D density patches for inhomogeneous Navier-Stokes,
    with F. Gancedo. Archive for Rational Mechanics and Analysis, 229 (1), 339-360, (2018). (Link to ArXiv)
  9. Global regularity for 2D Boussinesq temperature patches with no diffusion,
    with F. Gancedo. Annals of PDE 3, 14, (2017). (Link to ArXiv)

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