  Hydrodynamic systems arising in swarming modelling include nonlocal forces in
the form of attractive-repulsive potentials as well as pressure terms modelling
strong local repulsion. We focus on the case where there is a balance between
nonlocal attraction and local pressure in presence of confinement in the whole
space. Under suitable assumptions on the potentials and the pressure functions,
we show the global existence of weak solutions for the hydrodynamic model with
viscosity and linear damping. By introducing linear damping in the system, we
ensure the existence and uniqueness of stationary solutions with compactly
supported density, fixed mass and center of mass. The associated velocity field
is zero in the support of the density. Moreover, we show that global weak
solutions converge for large times to the set of these stationary solutions in
a suitable sense. In particular cases, we can identify the limiting density
uniquely as the global minimizer of the free energy with the right mass and
center of mass.
