A nonlinear toy model in kinetic theory

In this talk, I will present a recent joint work with C. Mouhot. It concerns a toy non-linear model in kinetic theory. We will see that the problem is globally well-posed in Sobolev spaces. The construction of solutions rely on some recent Hoelder estimates obtained with F. Golse, C. Mouhot and A. Vasseur combined with appropriate Schauder estimates.