neutron star resides in the neutron fluid and it plays the main role in the hydrodynamic oscillations of the star. Charged superfluids will be absorbed in the normal fluid of the star formally, as they are coupled to the electron liquid via electro-magnetic forces on short time-scales. Note that their role is crucial in controlling the mutual friction on the local hydrodynamic scale; however the physics of this scale will enter the theory on the global scale via phenomenological constants, which we will treat as free parameters of the theory.

Two-fluid Newtonian superfluid hydrodynamics
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The superfluid phases in neutron stars coexist with normal fluids whose interaction with superfluid vortices leads to the effect of the [*mutual friction*]{} between a superfluid and normal fluid. A phenomenological description of this effect is based on the two-fluid dissipative hydrodynamics. A particularly simple and transparent formulation which, with some care, can be taken over to describe superfluids in neutron stars, was developed by Bekarevich and Khalatnikov for liquid He$^4$ [@BK]. It is interesting that the general form of mutual friction forces can be obtained by utilizing only the conservation laws and some reasonable assumptions on the form of the dissipation. Although the superfluids 