From mean field games to Navier-Stokes equations. (English) Zbl 1520.91051
Summary: This work establishes the equivalence between mean field game and a class of PDE systems closely related to compressible Navier-Stokes equations. The solvability of the PDE system via the existence of the Nash equilibrium of the mean field game is provided under a set of conditions.
MSC:
| 91A16 | Mean field games (aspects of game theory) |
| 35Q30 | Navier-Stokes equations |
| 35Q89 | PDEs in connection with mean field game theory |
| 35F21 | Hamilton-Jacobi equations |
Keywords:
mean field game; Navier-Stokes equation; Hamilton-Jacobi-Bellman equation; Feynman-Kac formulaReferences:
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