# Maja Taskovic : Tail behavior of solutions to the Boltzmann equation

The Boltzmann equation models the evolution of the probability density of gas particles that interact through predominantly binary collisions. The equation consists of a transport operator and a collision operator. The latter is a bilinear integral with a non-integrable angular kernel. For a long time the equation was simplified by assuming that the kernel is integrable (so called Grad's cutoff), with a belief that such an assumption does not affect the equation significantly. Recently, however, it has been observed that a non-integrable singularity carries regularizing properties, which motivates further analysis of the equation in this setting. We study the 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. We show how the singularity rate of the angular kernel affects the order of tails that can be propagated. The result uses Mittag-Leffler functions, which are a generalization of exponential functions. This is based on joint works with Alonso, Gamba, Pavlovic and with Gamba, Pavlovic.

**Category**: Applied Math and Analysis**Duration**: 01:34:49**Date**: November 16, 2015 at 4:25 PM**Views**: 105-
**Tags:**seminar, Applied Math And Analysis Seminar

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