  We study a global well-posedness of measure-valued solutions to the kinetic
Lohe Hermitian sphere(LHS) model derived from the Lohe tensor(LT) model on the
set of rank-1 complex tensors(i.e. complex vectors) with the same size and
investigate emergent behaviors. The kinetic LHS model corresponds to a complex
analogue of the kinetic LS model which has been extensively studied in the
literature on the aggregation modeling of Lohe particles on the unit sphere in
Euclidean space. In this paper, we provide several frameworks in terms of
system parameters and initial data leading to the local and global
well-posedness of measure-valued solutions. In particular, we show emergent
behaviors of the kinetic LHS model with the same free flows by analyzing the
temporal evolution of the order parameter.
