Incompressible Navier-Stokes limit for the Enskog equation Original Research Article

The macroscopic limit of the Enskog kinetic equation with three small parameters: the Knudsen number, the Mach number, and the scale of the diameter of the particles, is considered in View the MathML source3. For some relations between the small parameters, the Enskog equation results in the Navier-Stokes equation for incompressible fluids completed by the Boussinesq relation and the temperature fluctuations equation. The global existence of classical solutions of the Enskog equation and convergence towards the macroscopic system are proved for small initial data (but independent of the small parameters).