  We study first order evolutive Mean Field Games whose operators are
non-coercive. This situation occurs, for instance, when some directions are
`forbidden' to the generic player at some points. Under some regularity
assumptions, we establish existence of a weak solution of the system. Mainly,
we shall describe the evolution of the population's distribution as the
push-forward of the initial distribution through a flow, suitably defined in
terms of the underlying optimal control problem.
