Infinite energy solutions to the homogeneous Boltzmann equation
Analysis of PDEs
2009-07-13 v1 Mathematical Physics
math.MP
Abstract
The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of probability measures defined via the Fourier transform. In that space, the second moment of a measure is not assumed to be finite, so infinite energy solutions are not {\it a priori} excluded from our considerations. Moreover, we study the large time asymptotics of solutions and, in a particular case, we give an elementary proof of the asymptotic stability of self-similar solutions obtained by A.V. Bobylev and C. Cercignani [J. Stat. Phys. {\bf 106} (2002), 1039--1071].
Keywords
Cite
@article{arxiv.0907.1676,
title = {Infinite energy solutions to the homogeneous Boltzmann equation},
author = {Marco Cannone and Grzegorz Karch},
journal= {arXiv preprint arXiv:0907.1676},
year = {2009}
}