Some remarks on a modified fluid dynamics equation

A modification of Navier-Stokes equation, recently suggested to overcome the well-known paradox about the sound diffusion with infinite velocity in viscous fluids, is compared with Navier-Stokes equation itself. Necessary and sufficient conditions to get common solutions of both are stated and consequences are pointed out. In the case of highly conducting ideal fluids embedded in a magnetic field, a supplementary effect is found related to classical magnetosonic waves.