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


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.