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Fluid dynamic limits for gas mixture I: Formal derivations. (English) Zbl 1152.82017

Summary: A macroscopic limit for a binary gas mixture in terms of the Boltzmann system with three small parameters: the Knudsen number, the Mach number and the diameter of particles, is considered in the whole physical space. When the small positive parameter \(\varepsilon\) goes to zero, it is shown that the Boltzmann system results in the compressible Euler equations decoupled with Navier-Stokes equations. In this first part of our paper, the results are of a conditional (formal) nature: both existence of a solution and existence of appropriate limits are assumed.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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