  Classical Navier-Stokes equations fail to describe some flows in both the
compressible and incompressible configurations. In this article, we propose a
new methodology based on transforming the fluid mass velocity vector field to
obtain a new class of continuum models. We uncover a class of continuum models
which we call the re-casted Navier-Stokes. They naturally exhibit the physics
of previously proposed models by different authors to substitute the original
Navier-Stokes equations. The new models unlike the conventional Navier-Stokes
appear as more complete forms of mass diffusion type continuum flow equations.
They also form systematically a class of thermo-mechanically consistent
hydrodynamic equations via the original equations. The plane wave analysis is
performed to check their linear stability under small perturbations, which
confirms that all re-casted models are spatially and temporally stable like
their classical counterpart. We then use the Rayleigh-Brillouin scattering
experiments to demonstrate that the re-casted equations may be better suited
for explaining some of the experimental data where original Navier-Stokes fail.
