  The spatially inhomogeneous large $N$ solutions to Kazakov--Migdal model are
analyzed. The set of nonlinear differential equations is derived in the
continuum limit. In one dimensional case these equations has a natural
interpretation in terms of the dynamics of a Fermi gas. The multidimensional
case seems to be inconsistent because of its instability related to the
collapse of eigenvalues of the scalar field.
