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Let$U$be an open subset of a complex locally convex space$E$, and$H(U)$the space of holomorphic functions from$U$to$C$. If the dual$E′$of$E$is nuclear with respect to the topology generated by the absolutely convex compact subsets of$E$, then it is shown that$H(U)$endowed with the compact open topology is a nuclear space. In particular, if$E$is the strong dual of a Fréchet nuclear space, then$H(U)$is a Fréchet nuclear space.

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In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view of its possible extensions to other kinds of collective motion.