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

Emergent behaviors of the kinetic Lohe Hermitian sphere model