  It is often assumed that the strong gravitational field of a super-massive
black hole disrupts an adjacent molecular cloud preventing classical star
formation in the deep potential well of the black hole. Yet, young stars have
been observed across the entire nuclear star cluster of the Milky Way including
the region close ($<$0.5~pc) to the central black hole, Sgr A*. Here, we focus
particularly on small groups of young stars, such as IRS 13N located 0.1 pc
away from Sgr A*, which is suggested to contain about five embedded massive
young stellar objects ($<$1 Myr). We perform three dimensional hydrodynamical
simulations to follow the evolution of molecular clumps orbiting about a
$4\times10^6~M_{\odot}$ black hole, to constrain the formation and the physical
conditions of such groups. The molecular clumps in our models assumed to be
isothermal containing 100 $M_{\odot}$ in $<$0.2 pc radius. Such molecular
clumps exist in the circumnuclear disk of the Galaxy. In our highly
eccentrically orbiting clump, the strong orbital compression of the clump along
the orbital radius vector and perpendicular to the orbital plane causes the gas
densities to increase to values higher than the tidal density of Sgr A*, which
are required for star formation. Additionally, we speculate that the infrared
excess source G2/DSO approaching Sgr A* on a highly eccentric orbit could be
associated with a dust enshrouded star that may have been formed recently
through the mechanism supported by our models.
