Infinite energy solutions to the homogeneous Boltzmann equation

Details Infinite energy solutions to the homogeneous Boltzmann equation Infinite energy solutions to the homogeneous Boltzmann equation

2009-07-09

arxiv.org/abs/0907.1676v1

Mathematics

Analysis of PDEs

Scientific paper

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].

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