We study the evolution and observability of young, compact star clusters near the Galactic center, such as the Arches and Quintuplet systems. The clusters are modeled by integrating the equations of motion of all stars while accounting for the internal evolution of the stars and binaries and the effect of the tidal field of the Galaxy. We find that clusters within 150 pc of the Galactic center dissolve within 55 Myr, but their projected densities drop below the background density in the direction of the Galactic center within only a few Myr, effectively making these clusters undetectable after that time. Detailed observations of the Arches cluster, when taken at face value, suggest that its mass function is unusually flat and that the cluster contains an overabundance of stars more massive than 20Mo. Our dynamical analysis, however, shows that the observed characteristics of the Arches cluster are consistent with a perfectly normal initial mass function. The observed anomalies are caused by a combination of observational selection effects and the dynamical evolution of the cluster. We calibrate the current parameters of the Arches cluster using a normal initial mass function and conclude that the cluster is more massive than 40000 o has a half mass radius of about 0.35 pc, and is located between 50 and 90 pc from the Galactic center.