Article Contents
Article Contents

# On self-similar solutions to the homogeneous Boltzmann equation

• 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.
Mathematics Subject Classification: Primary: 82C40; Secondary: 76P05.

 Citation:

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