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. Accepted in Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 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. Advances in Mathematics, 399, (2022). (Link to ArXiv).
  4. The Peskin Problem with Viscosity Contrast, with Y. Mori, R. Strain. To appear 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. To appear in Memoirs of the American Mathematical Society, 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)

Research profiles: ArXiv, ORCID, Google ScholarResearchGate, Scopus, Web of ScienceMathSciNet. Information about talks, workshops and grants can be found in my Curriculum Vitae.