Compressible Navier-Stokes limit of binary mixture of gas particles

In this paper we study the compressible Navier-Stokes limit of binary mixture of gas particles in which a species is dense and the other is sparse. Their collisions are decided by Grad's hard potentials. When the Knudsen number of dense species of the Boltzmann system goes to zero, we show that the hydrodynamic variables satisfy compressible Navier-Stokes type equations. It turns out that the macro fluid variables corresponding to the dense species satisfy the standard compressible Navier-Stokes equations. But the fluid equations for sparse species contain influence terms of dense species. Like single species gas, we employed Enskog-Chapman and moment methods up to the first order.