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### Scattering Theory for the Boltzmann Equation and the Arrow of Time

**GGAM Colloquium**

Speaker: | C. David Levermore, University of Maryland |

Related Webpage: | http://www.math.umd.edu/~lvrmr |

Location: | 1147 MSB |

Start time: | Fri, Mar 6 2015, 4:10PM |

We develop a scattering theory for a class of eternal solutions of the Boltzmann equation posed over all space. In three spatial dimensions each of these solutions has thirteen conserved quantities. The Boltzmann entropy has a unique minimizer with the same thirteen conserved values. This minimizer is a local Maxwellian that is also a global solution of the Boltzmann equation --- a so-called global Maxwellian. We show that each of our eternal solutions has a streaming asymptotic state as time goes to minus or plus infinity. However it does not converge to the associated global Maxwellian as time goes to infinity unless it is that global Maxwellian. The Boltzmann entropy decreases as time increases, but does not decrease to its minimum as time goes to infinity. Said another way, the final step in the traditional argument for the heat death of the universe is not valid. This is joint work with Claude Bardos, Irene Gamba, and Francois Golse.

Reception to follow the lecture