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

摘要

In this paper we investigate an optimal control problem in the space of measures on ?~2. 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 Hamilton- Jacobi-Bellman equation, in the space of probability measures, is well posed in an appropriately defined viscosity solution sense.