Charles Elbar (Université Claude Bernard - Lyon 1) : Sobolev bounds in the Keller-Segel system

Abstract: The Keller-Segel system was derived to model chemotaxis, the process by which cells detect signals in their environment and adjust their movement accordingly. In this talk, I will present a method to prove uniform W^{1,p} Sobolev bounds for all p on the solutions, by computing the dissipation of a functional appearing in the Bakry-Emery theory. Controlling this dissipation requires proving a functional inequality in the spirit of the Brezis-Gallouët inequality since classical sobolev embeddings are not enough.