We study the evolution and observability of young and compact star clusters near the Galactic center, such as the Arches cluster and the Quintuplet. The star clusters are modeled with a combination of techniques; using direct \nbody integration to calculate the motions of all stars and detailed stellar and binary evolution to follow the evolution of the stars. The modeled star clusters dissolve within 10 to 60 million years in the tidal field of the Galaxy. The projected stellar density in the modeled clusters drops within 5% to 70% of the lifetime to a level comparable to the projected background density towards the Galactic center. And it will be very hard to distinguished these clusters at later age among the background stars. This effect is more severe for clusters at larger distance from the Galactic center but in projection at the same distance. Based on these arguments we conclude that the Galactic center easily hides 10 to 40 clusters with characteristics similar to the Arches and the Quintuplet cluster.