  We present results for transport properties (diffusion and viscosity) using
computer simulations. Focus is made on a densified binary sodium disilicate
2SiO$_2$-Na$_2$O (NS2) liquid and on multicomponent magmatic liquids (MORB,
basalt). In the NS2 liquid, results show that a certain number of anomalies
appear when the system is densified: the usual diffusivity maxima/minima is
found for the network-forming ions (Si,O) whereas the sodium atom displays
three distinct r\'egimes for diffusion. Some of these features can be
correlated with the obtained viscosity anomaly under pressure, the latter being
be fairly well reproduced from the simulated diffusion constant. In model
magmas (MORB liquid), we find a plateau followed by a continuous increase of
the viscosity with pressure. Finally, having computed both diffusion and
viscosity independently, we can discuss the validity of the Eyring equation for
viscosity which relates diffusion and viscosity. It is shown that it can be
considered as valid in melts with a high viscosity. On the overall, these
results highlight the difficulty of establishing a firm relationship between
dynamics, structure and thermodynamics in complex liquids.
