Amic Frouvelle
Biography
Short bio: Amic Frouvelle, Ceremade (Université Paris Dauphine - PSL). Interested in modeling and analysis of models of collective behaviour.
Title: Hypocoercivity in a model of aligning self-propelled particles
Abstract: This talk is about a joint work with Emeric Bouin. We are interested in the long-time behavior of the kinetic Vicsek equation with phase transition, in its spatially localized version. The method follows the now-classic approach of modifying Sobolev-type norms by adding cross-terms, linked to commutators between the different operators appearing in the kinetic equation. However, the fact that the velocity space is the sphere adds significant subtleties and requires to develop an adapted algebraic framework of operators. Taking advantage of this new framework, we manage to perform an approach à la Hérau to show the nonlinear stability.
