Abstract
We study the Cauchy problem for the spatially homogenem Boltzmann equation for true Maxwell molecules. Using the Fourier representation introduced by Bobylev [Bo75],we give a simplified proof of a result proved by Tanaka [Ta78].Moreover, we show by means of simple geometric properties, that Tanaka functional is an entropy decreasing functional for the Boltzmann equation for Maxwell molecules.
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Pulvirenti, A., Toscani, G. The theory of the nonlinear Boltzmann equation for Maxwell molecules in Fourier representation. Annali di Matematica pura ed applicata 171, 181–204 (1996). https://doi.org/10.1007/BF01759387
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DOI: https://doi.org/10.1007/BF01759387