Extra mass flux in fluid mechanics

The conditions of existence of extra mass flux in single component dissipative non-relativistic fluids are clarified. By considering Galilean invariance we show that if total mass flux is equal to total momentum density, then mass, momentum, angular momentum and booster (center-of-mass) are conserved. However, these conservation laws may be fulfilled also by other means. We show an example of weakly non-local hydrodynamics where the conservation laws are satisfied as well although the total mass flux is different from momentum density.