  We consider maps between Riemannian manifolds in which the map is a
stationary point of the nonlinear Hodge energy. The variational equations of
this functional form a quasilinear, nondiagonal, nonuniformly elliptic system
which models certain kinds of compressible flow. Conditions are found under
which singular sets of prescribed dimension cannot occur. Various degrees of
smoothness are proven for the sonic limit, high-dimensional flow, and flow
having nonzero vorticity. The gradient flow of solutions is estimated.
Implications for other quasilinear field theories are suggested.
