  We introduce exact analytical solutions of the steady-state hydrodynamic
equations of scale-free, self-gravitating gaseous disks with flat rotation
curves. We express the velocity field in terms of a stream function and obtain
a third-order ordinary differential equation (ODE) for the angular part of the
stream function. We present the closed-form solutions of the obtained ODE and
construct hydrodynamical counterparts of the power-law and elliptic disks, for
which self-consistent stellar dynamical models are known. We show that the
kinematics of the Large Magellanic Cloud can well be explained by our findings
for scale-free elliptic disks.
