The theory of the nonlinear Boltzmann equation for Maxwell molecules in Fourier representation

We study the Cauchy problem for the spatially homogenem Boltzmann equation for true Maxwell molecules. Using the Fourier representation introduced byBobylev [Bo75],we give a simplified proof of a result proved byTanaka [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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