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

Feng, Jin; Święch, Andrzej

doi:10.1090/S0002-9947-2013-05634-6

Optimal control for a mixed flow of Hamiltonian and gradient type in space of probability measures
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by Jin Feng and Andrzej Święch; with Appendix B by Atanas Stefanov PDF

Trans. Amer. Math. Soc. 365 (2013), 3987-4039 Request permission

Abstract:

In this paper we investigate an optimal control problem in the space of measures on $\mathbb {R}^2$. 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.

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