Abstract
We consider time-dependent mean-field games with congestion that are given by a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton-Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C-infinity solutions for sub-quadratic Hamiltonians.