Infinite energy solutions to the homogeneous Boltzmann equation
Marco Cannone, Grzegorz Karch
Source abstract
Abstract The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel that 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 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. 106 (2002), 1039–1071]. © 2009 Wiley Periodicals, Inc.
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