My research interests lie within analysis, partial differential equations and fluid mechanics. More specifically, I am interested in the evolution of moving incompressible fluid interfaces coming from physical models.
During my graduate career, I have studied the global well-posedness and interface regularity for patch problems in nonlinear parabolic equations such as Navier-Stokes and Boussinesq. I have also worked on the Muskat problem, addressing additional questions like large-time decay of solutions or ill-posedness.
A brief summary of my current research can be found in this short version of my ResearchStatement. I am always avalaible through email for more information (firstname.lastname@example.org).
- Global regularity for 2D Boussinesq temperature patches with no diffusion,
with F. Gancedo. Ann. PDE (2017), 3: 14. (Link to ArXiv)
- Global regularity of 2D density patches for inhomogeneous Navier-Stokes,
with F. Gancedo. Arch. Ration. Mech. Anal. (2018), 229:339. (Link to ArXiv)
- On the Muskat problem with viscosity jump: Global in time results,
with F. Gancedo, N. Patel and R. Strain. Adv. Math., Vol. 345, P. 552-597, (2019). (Link to ArXiv)
- Regularity results for viscous 3D Boussinesq temperature fronts, with F. Gancedo. Submitted, arXiv:1809.00701, (2018). (Link to ArXiv)
- Global Regularity for Gravity Unstable Muskat Bubbles, with F. Gancedo, N. Patel and R. Strain. Submitted, arXiv:1902.02318, (2019). (Link to ArXiv)