From kinetic to Navier-Stokes-type equations Original Research Article

Some kinetic equations with symmetrized kernels in a box are considered. It is shown that, for a particular choice of relations between the small parameters of the models, the equations result in the Navier-Stokes-type system for compressible fluids at the 0th order approximation. The viscosity and heat conduction terms, in the resulting system, are independent of the small parameters. It is proved that the existence of smooth solutions of the Navier-Stokes-type system implies both existence of solutions to the kinetic equations and asymptotic relationship.