Small mass ratio limit of Boltzmann equations in the Context of the study of evolution of dust particles in a rarefied atmosphere
The paper analyzes the evolution of particles of a dust in a rarefied atmosphere. This topic can be found in the context of safety studies for the ITER project of nuclear fusion. When the typical size of a dust particle becomes too large compared to that of a molecule of the gas, the corresponding numerical simulation becomes too expensive. Consequently, one needs to introduce an asymptotic model, in which the ratio of the gas-molecule mass to the dust-particle mass tends to zero. In order to obtain such a model, the paper considers a system of two Boltzmann equations for the distribution function of the gas molecules and distribution function of the dust particles. The latter function depends not only on the position and velocity but also on the particle radius, which can vary in a certain interval. The main result of the work is that, when the proposed model is spatially homogeneous, the model is, in the aforementioned limit case, reduced to a system of two equations of the Vlasov-Boltzmann type. The system is simpler and admits more effective numerical treatment. The passage to the limit is rigorously proven. The proof includes a new version of Povzner's inequality in which the vanishing mass ratio is taken into account.
scientific article; zbMATH DE number 5655379