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.

Publications:

  1. Desingularization of small moving corners for the Muskat equation, with J. Gómez-Serrano, S. V. Haziot, B. Pausader. Submitted, arXiv:2305.05046, (2023).
  2. Well-Posedness of the 3D Peskin Problem, with P.-C. Kuo, Y. Mori, R. Strain. Submitted, arXiv:2301.12153, (2023).
  3. Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast, with F. Gancedo. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, (2021). (Link to ArXiv)
  4. Quantitative Hölder Estimates for Even Singular Integral Operators on Patches, with F. Gancedo. Journal of Functional Analysis, 283 (9), (2022). (Link to ArXiv)
  5. Self-similar solutions for the Muskat equation, with J. Gómez-Serrano, H. Q. Nguyen, B. Pausader. Advances in Mathematics, 399, (2022). (Link to ArXiv).
  6. The Peskin Problem with Viscosity Contrast, with Y. Mori, R. Strain. To appear in Analysis & PDE, arXiv:2009.03360, (2020). (Link to ArXiv)
  7. 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)
  8. Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo.  Communications in Mathematical Physics, 376, 1705-1736 (2020). (Link to ArXiv)
  9. 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)
  10. 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)
  11. 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 Scholar,  ResearchGate, Scopus, Web of Science,  MathSciNet. Information about talks, workshops and grants can be found in my Curriculum Vitae.