Young Researchers Workshop: Kinetic models in biology and social sciences

Exponential tails for the non-cutoff Boltzmann equation

Maja Taskovic

University of Pennsylvania

In this talk we will discuss behavior in time of tails of solutions to the Boltzmann equation in the non-cutoff regime, by examining the generation and propagation in time of L^1 and L^\infty exponentially weighted estimates and the relation between them. For this purpose we introduce Mittag-Leffler moments, which can be understood as a generalization of exponential moments. An interesting aspect of the result is that the singularity rate of the angular kernel affects the order of tails that can be propagated in time. This is based on joint works with Alonso, Gamba, Pavlovic and with Gamba, Pavlovic.