Existence and uniqueness of minimizers in variational problems (Wilfrid Gangbo, UCLA)

We comment on the main steps to take when studying some variational problems. This includes optimization problems arising in geometry, machine learning, non linear elasticity, fluid mechanics, etc… For the sake of illustration, in this talk, we keep our focus on a minimization problem obtained after a time-discretization of the incompressible Navier-Stokes equations. Elementary geometric intuitions are used to uniquely characterize equilibria which are minimizers.