  In this article, a suite of physically inconsistent properties of the
Navier-Stokes equations, associated with the lack of mass diffusion and the
definition of velocity, are presented. We show that these inconsistencies are
consequences of the Lagrangian derivation that models viscous stresses rather
than diffusion. A new model for compressible and diffusive (viscous and heat
conducting) flows of an ideal gas, is derived in a purely Eulerian framework.
We propose that these equations supersede the Navier-Stokes equations. A few
numerical experiments demonstrate some differences and similarities between the
new system and the Navier-Stokes equations.
