A Boltzmann Equation with Stochastic Kinetic Transport

The classical Boltzmann equation provides a mesoscopic description of a large number of identical, interacting particles. Namely, it is an evolution equation for the particle density which accounts for both free transport and binary collisions. In this talk, we discuss a variant of the classical model in which particles undergo a stochastic transport mechanism in between collisions. This may be interpreted as accounting for an external random field, or background noise acting on the particles. We focus in particular on the well posedness of the mesocopic, stochastic PDE description of the system. Our main result is the global existence of so-called renormalized, weak martingale solutions. This is a joint work with Sam Punshon-Smith (UMD-College Park).