Infinite energy solutions to the homogeneous Boltzmann equation

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.