# Francisco

# Gancedo

###### RESEARCHER

Francisco Gancedo performed his doctoral studies under the direction of D Córdoba (ICMAT-CSIC) in the U Autónoma de Madrid. Next, he held an L.E. Dickson Instructor at the U Chicago for four years.

He was a Ramón y Cajal Assistant Professor at the US. He is an Associate Professor at the Department of Mathematical Analysis at the US. His research line focuses on the mathematical analysis of the formation and propagation of singularities for incompressible fluids, strongly linked to the analysis of the Navier-Stokes equations, one of the Clay Mathematics Institute Millennium problems.

He studies different physical models for their mathematical interest as well as for their applications. In the analysis of fluid mechanics, an outstanding class of problems are those in which the evolution of fluids with different characteristics is modelled. The motion takes place on the interface between fluids that evolves with the flow. These problems are given by fundamental fluid mechanics laws, such as Euler and Navier-Stokes equations, Darcy's law and Quasi-geostrophic systems. These give rise to problems such as vortex sheets, water and viscous waves, Muskat, Hele-Shaw and evolution of sharp fronts. The fundamental questions to address are local-existence, uniqueness, global-existence of solution or formation of singularities. With the new techniques developed by him and collaborators, it is now possible to prove finite-time singularity formation for some scenarios in Muskat, water waves, Navier-Stokes, and sharp fronts of temperature. These are the first analytic proofs of blow-up for incompressible fluids in well-posed situations. He has experience as PI in several scientific projects, as a grant of the National Science Foundation DMS-0901810 from 2009 to 2012 and an ERC Starting Grant (Fluid-Interface 639227) starting in 2015.