  Stellar kinematics is a powerful tool for understanding the formation process
of stellar associations. Here, we present a kinematic study of the young
stellar population in the Rosette nebula using the recent Gaia data and
high-resolution spectra. We first isolate member candidates using the published
mid-infrared photometric data and the list of X-ray sources. A total of 403
stars with similar parallaxes and proper motions are finally selected as
members. The spatial distribution of the members shows that this star-forming
region is highly substructured. The young open cluster NGC 2244 in the center
of the nebula has a pattern of radial expansion and rotation. We discuss its
implication on the cluster formation, e.g., monolithic cold collapse or
hierarchical assembly. On the other hand, we also investigate three groups
located around the border of the H II bubble. The western group seems to be
spatially correlated with the adjacent gas structure, but their kinematics is
not associated with that of the gas. The southern group does not show any
systematic motion relative to NGC 2244. These two groups might be spontaneously
formed in filaments of a turbulent cloud. The eastern group is spatially and
kinematically associated with the gas pillar receding away from NGC 2244. This
group might be formed by feedback from massive stars in NGC 2244. Our results
suggest that the stellar population in the Rosette Nebula may form through
three different processes: the expansion of stellar clusters, hierarchical star
formation in turbulent clouds, and feedback-driven star formation.
