Optimal control for a mixed flow of Hamiltonian and gradient type in space of probability measures

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Abstract. In this paper we investigate an optimal control problem in the space of measures on R2. The problem is motivated by a stochastic interacting particle model which gives the 2-D Navier-Stokes equations in their vorticity formulation as a mean-field equation. We prove that the associated HamiltonJacobi-Bellman equation, in the space of probability measures, is well posed in an appropriately defined viscosity solution sense.