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.
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