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Some applications of the method of moments for the homogeneous Boltzmann and Kac equations. (English) Zbl 0784.76081

Summary: Using the method of moments, we prove that any polynomial moment of the solution of the homogeneous Boltzmann equation with hard potentials or hard spheres is bounded provided that a moment of order strictly higher than 2 exists initially. We also give partial results on convergence towards the Maxwellian equilibrium in the case of soft potentials. Finally, exponential as well as Maxwellian estimates are introduced for the Kac equation.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
45K05 Integro-partial differential equations
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