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.
- Desingularization of small moving corners for the Muskat equation, with J. Gómez-Serrano, S. V. Haziot, B. Pausader. Submitted, arXiv:2305.05046, (2023).
- Well-Posedness of the 3D Peskin Problem, with P.-C. Kuo, Y. Mori, R. Strain. Submitted, arXiv:2301.12153, (2023).
- 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)
- Quantitative Hölder Estimates for Even Singular Integral Operators on Patches, with F. Gancedo. Journal of Functional Analysis, 283 (9), (2022). (Link to ArXiv)
- Self-similar solutions for the Muskat equation, with J. Gómez-Serrano, H. Q. Nguyen, B. Pausader. Advances in Mathematics, 399, (2022). (Link to ArXiv).
- The Peskin Problem with Viscosity Contrast, with Y. Mori, R. Strain. To appear in Analysis & PDE, arXiv:2009.03360, (2020). (Link to ArXiv)
- 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)
- Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo. Communications in Mathematical Physics, 376, 1705-1736 (2020). (Link to ArXiv)
- 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)
- 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)
- 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.