A maxwellian lower bound for solutions to the Boltzmann equation |
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Authors: | Ada Pulvirenti Bernt Wennberg |
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Institution: | 1. Dipartimento di Matematica, Università di Pavia, Via Abbiategrasso 215, 27100, Pavia, Italy 2. Department of Mathematics, Chalmers University of Technology, 41296, G?teborg, Sweden
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Abstract: | We prove that the solution of the spatially homogeneous Boltzmann equation is bounded pointwise from below by a Maxwellian,
i.e. a function of the formc
1 exp(-c
2
v
2). This holds for any initial data with bounded mass, energy and entropy, and for any positive timet≧t
0. The constantsc
1, andc
2, depend on the mass, energy and entropy of the initial data, and ont
0>0 only.
A similar result is obtained for the Kac caricature of the Boltzmann equation, where the proof is easier. |
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Keywords: | |
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