2016/05/05 by David M. Ambrose, Ambrose, David M. · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1605.01745
openalex publication_date 2016/05/05 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
We prove existence theorems for strong solutions of time-dependent mean field\ngames with non-separable Hamiltonian. In a recent announcement, we showed\nexistence of small, strong solutions for mean field games with local coupling.\nWe first generalize that prior work to allow for non-separable Hamiltonians.\nThis proof is inspired by the work of Duchon and Robert on the existence of\nsmall-data vortex sheets in incompressible fluid mechanics. Our next existence\nresult is in the case of weak coupling of the system; that is, we allow the\ndata to be of arbitrary size, but instead require that the (still possibly\nnon-separable) Hamiltonian be small in a certain sense. The proof of this\ntheorem relies upon an appeal to the implicit function theorem.\n