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This work establishes the equivalence between Mean Field Game and a class of compressible Navier-Stokes equations for their connections by Hamilton-Jacobi-Bellman equations. The existence of the Nash Equilibrium of the Mean Field Game, and hence the solvability of Navier-Stokes equations, are provided under a set of conditions.
In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is brought to be
In this paper we study second order master equations arising from mean field games with common noise over arbitrary time duration. A classical solution typically requires the monotonicity condition (or small time duration) and sufficiently smooth dat
We study first order evolutive Mean Field Games where the Hamiltonian is non-coercive. This situation occurs, for instance, when some directions are forbidden to the generic player at some points. We establish the existence of a weak solution of the
In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that satisfy a
We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory, construct