  A fluid-dynamic approach to the diffusion of heavy quarks in the quark--gluon
plasma (QGP) is presented. Specifically, we analyze the Fokker-Planck equation
for the momentum transport of heavy quarks from a fluid perspective and use a
mapping to second-order fluid-dynamics to determine conductivities and
relaxation times governing their spatial diffusion. By investigating the
relation between the two approaches, we provide new insights concerning the
level of local thermalization of charm and bottom quarks inside the expanding
QGP. Our results indicate that a fluid-dynamic description of diffusion is
feasible for charm quarks at least for the latest stages of the fireball
evolution.
