  The dynamics of a confined fluid of Bose atoms is treated within the linear
response regime, with a view to establishing a current-density functional
formalism for an inhomogeneous superfluid state. After evaluating in full
detail a simplified case of an external coupling to the density and phase of
the condensate, the theory is extended to include the coupling to the total
current density. The Kohn-Sham response functions of the condensate and all the
exchange-correlation kernels for the superfluid are introduced from the
microscopic equations of motion and are expressed in a physically transparent
way through functional derivatives of correlation functions. A microscopic
formula for the superfluid density is derived and used to introduce a
generalized hydrodynamic approach for a weakly inhomogeneous two-fluid model in
isothermal conditions. Local-density expressions are thereby derived for the
velocities of first and second sound in the weakly inhomogeneous superfluid and
for visco-elastic functions describing the transition from the hydrodynamic to
the collisionless regime. Landau's hydrodynamic theory and known results in
Green's functions language are recovered in the limiting case of a homogeneous
superfluid.
