  We use kinetic theory and the thermodynamic Bethe ansatz to derive the
hydrodynamics of spin transport in the Haldane-Shastry chain. We obtain
analytical expressions for relaxation from weak-domain-wall initial conditions
and corresponding predictions for the spin Drude weight. We corroborate the
latter against an exact microscopic calculation at infinite temperature and
Luttinger-liquid expectations at zero temperature. We further obtain an
analytical expression for the long-wavelength dynamics of the longitudinal spin
structure factor at all fillings and temperatures. We show that the latter
interpolates between an empirically exact expression that we have found at
infinite temperature and the long-wavelength limit of the Haldane-Zirnbauer
formula at zero temperature.
