# American Institute of Mathematical Sciences

December  2013, 6(4): 801-808. doi: 10.3934/krm.2013.6.801

## On self-similar solutions to the homogeneous Boltzmann equation

 1 Université Paris-Est-Marne-la-Vallée, Laboratoire d'Analyse et de Mathématiques Appliquées, UMR 8050 CNRS, 5 boulevard Descartes, Cité Descartes Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France 2 Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Received  July 2013 Revised  August 2013 Published  November 2013

In this note, our results from [ Comm. Pure Appl. Math. 63 (2010), 747--778] on infinite energy solutions to the homogeneous Boltzmann equation for Maxwellian-type molecules are discussed, presented in a different context, and improved by using recent observations by Morimoto and Yang. In particular, similarities between the homogeneous Boltzmann equation and the fractional heat equation are emphasized. Moreover, we show that a certain conjecture by Bobylev and Cercignani on regularity of self-similar solutions to the homogeneous Boltzmann equation for Maxwellian-type molecules has a positive answer.
Citation: Marco Cannone, Grzegorz Karch. On self-similar solutions to the homogeneous Boltzmann equation. Kinetic & Related Models, 2013, 6 (4) : 801-808. doi: 10.3934/krm.2013.6.801
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