A maxwellian lower bound for solutions to the Boltzmann equation

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 formc1 exp(-c2v2). This holds for any initial data with bounded mass, energy and entropy, and for any positive timet≧t0. The constantsc1, andc2, depend on the mass, energy and entropy of the initial data, and ont0>0 only.A similar result is obtained for the Kac caricature of the Boltzmann equation, where the proof is easier.

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