Some remarks on a certain class of axisymmetric fluids of differential type

We prove global existence and uniqueness for axisymmetric solutions without swirl for the three-dimensional second grade fluid and the α-Euler equations. The domain considered is either a bounded domain (invariant with respect to rotations about some axis) or the full space R3. For a certain class of stationary solutions of the α-Euler equations Lyapunov stability is proved.