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We analyse the 2-dimensional Euler point vortices dynamics in the Koopman-VonNeumann approach. Classical results provide well-posedness of this dynamicsinvolving singular interactions for a finite number of vortices, on afull-measure set with respect to the volume measure $dx^N$ on the phase space,which is preserved by the measurable flow thanks to the Hamiltonian nature ofthe system. We identify a core for the generator of the one-parameter group ofKoopman-Von Neumann unitaries on $L^2(dx^N)$ associated to said flow, the corebeing made of observables smooth outside a suitable set on which singularitiescan occur.

Essential Self-Adjointness of Liouville Operator for 2D Euler Point Vortices