Did the Boltzmann Equation Actually Converge to the Navier-Stokes Equation?

The Boltzmann equation was derived in 1872 by Austrian physicist Ludwig Boltzmann. The leading terms of this series look like the Navier-Stokes equation when a gas becomes denser and more fluid-like. In most fluids, capillarity is negligible compared to viscosity, but it isn't always, and mathematically, it never is. Carlin: "Something very much reminding us of the equations of Kordovich for the two-phase fluid"