Rigidity Vs. Viscosity and Bulk modulus

Can one consider a rigid body as a fluid having infinite viscosity and bulk modulus?

Basically, I am asking if is it possible to start from Navier-Stokes equations (including Bulk modulus and viscosity), take the proper limit and find that the motion (velocity vector field) is restricted to a rotating pattern at any given moment of time. i.e.
$$vec{v}(vec{r}, t)=vec{omega}(t)timesvec{r}+vec{v}_0(t)$$