On regularity and asymptotic behaviour of a spatially homogeneous Maxwell gas. (English) Zbl 0893.76081

Toscani, G.

Greco, Antonio M. (ed.) et al., The proceedings of the 8th international conference on Waves and stability in continuous media, held in Palermo, Italy, October 9–14, 1995. Part 1–2. Palermo: Circolo Matemático di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 45, 649-662 (1996).

We extend to the spatially homogeneous Boltzmann equation for a gas of Maxwellian pseudomolecules a method based on the central limit theorem. This method enables to control the regularity and the convergence towards equilibrium of the square root of the solution to the Boltzmann equation both in plane geometry, and in the axially symmetric case. Similar results were earlier obtained for the one-dimensional Kac equation, and in any dimension of the velocity space for the model Boltzmann equation.
For the entire collection see [Zbl 0863.00051].

MSC:

76P05	Rarefied gas flows, Boltzmann equation in fluid mechanics
82D05	Statistical mechanics of gases

Keywords:

Maxwellian pseudomolecules; central limit theorem; convergence; plane geometry; axially symmetric case