Young Researchers Workshop: Kinetic theory with applications in physical sciences

Exponential tail behavior for solutions to the homogeneous Boltzmann equation

Maja Taskovic

University of Pennsylvania
[SLIDES]

We study tail behavior of solutions to the spatially homogeneous Boltzmann equation for hard potentials with non-integrable angular cross section. We discuss the generation and propagation of $L^1$ and $L^infty$ exponentially weighted estimates and the relation between them. Order of tails that are propagated depend on the singularity rate of the angular cross-section. For some of those rates the corresponding functional weights are super-Gaussians, while for others the weights are Mittag-Leffler functions (fractional power series behaving asymptotically as super-Gaussians). This is based on joint works with Alonso, Gamba, Pavlovic and with Gamba, Pavlovic.