Fluid dynamic limits for gas mixture I. Formal derivations

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 is an element of 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.