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. F. Gancedo, E. García-Juárez, P. Luna-Velasco. On 2D Navier-Stokes free boundary: nonnegative density and small viscosity contrast. Preprint, arXiv:2507.09333, (2025).
  2. E. García-Juárez, P.-C. Kuo, Y. Mori. The Immersed Inextensible Interface Problem in 2D Stokes Flow. SIAM Journal on Mathematical Analysis, Vol. 57, 4 (2025).  (Link to ArXiv).
  3. F. Gancedo, E. García-Juárez, N. Patel, R. Strain. On Nonlinear Stability of Muskat Bubbles. Journal de Mathématiques Pures et Appliquées, Vol. 194, 103664, (2025). (Link to arXiv)
  4. E. García-Juárez, S. V. Haziot. Critical well-posedness for the 2D Peskin problem with general tension. Advances in Mathematics, 460, (2025). (Link to ArXiv).
  5. E. García-Juárez, P.-C. Kuo, Y. Mori, R. Strain. Well-Posedness of the 3D Peskin Problem. Mathematical Models and Methods in Applied Sciences, Vol. 35, No. 01, pp. 113-216, (2025). (Link to ArXiv)
  6. E. García-Juárez, J. Gómez-Serrano, S. V. Haziot, B. Pausader. Desingularization of small moving corners for the Muskat equation. Annals of PDE 10, 17, (2024). (Link to ArXiv)
  7. F. Gancedo, E. García-Juárez, N. Patel, R. Strain. Global Regularity for Gravity Unstable Muskat Bubbles. Memoirs of the American Mathematical Society, 292, no. 1455, (2023). (Link to ArXiv)
  8. E. García-Juárez, Y. Mori, R. Strain. The Peskin Problem with Viscosity Contrast. Analysis & PDE, Vol. 16, No. 3, 785-838, (2023). (Link to ArXiv)
  9. F. Gancedo, E. García-Juárez. Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast. Ann. Inst. H. Poincaré Anal. Non Linéaire 40, no. 6, pp. 1319–1352, (2023). (Link to ArXiv)
  10. E. García-Juárez, J. Gómez-Serrano, H. Q. Nguyen, B. Pausader. Self-similar solutions for the Muskat equation. Advances in Mathematics, 399, (2022). (Link to ArXiv).
  11. F. Gancedo, E. García-Juárez. Quantitative Hölder Estimates for Even Singular Integral Operators on Patches. Journal of Functional Analysis, 283 (9), (2022). (Link to ArXiv)
  12. F. Gancedo, E. García-Juárez. Regularity results for viscous 3D Boussinesq temperature fronts.  Communications in Mathematical Physics, 376, 1705-1736 (2020). (Link to ArXiv)
  13. F. Gancedo, E. García-Juárez, N. Patel, R. Strain. On the Muskat problem with viscosity jump: Global in time results. Advances in Mathematics, 345,  552-597, (2019). (Link to ArXiv)
  14. F. Gancedo, E. García-Juárez. Global regularity of 2D density patches for inhomogeneous Navier-Stokes. Archive for Rational Mechanics and Analysis, 229 (1), 339-360, (2018). (Link to ArXiv)
  15. F. Gancedo, E. García-Juárez. Global regularity for 2D Boussinesq temperature patches with no diffusion. 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.