NONFLU · Non-local dynamics in incompressible fluids

The goal of this project is to pursue new methods in the mathematical analysis of non-local and non-linearpartial differential equations. For this purpose we present several physical scenarios of interest in the contextof incompressible fluids, from a mathematical point of view as well as for its applications: both from thestandpoint of global well-posedness, existence and uniqueness of weak solutions and as candidates for blowup.The equations we consider are the incompressible Euler equations, incompressible porous media equationand the generalized Quasi-geostrophic equation. This research will lead to a deeper understanding of the natureof the set of initial data that develops finite time singularities as well as those solutions that exist for all time for incompressible flows.