  We study dispersive models of fluid flow in viscoelastic vessels, derived in
the study of blood flow. The unknowns in the models are the velocity of the
fluid in the axial direction and the displacement of the vessel wall from rest.
We prove that one such model has a well-posed initial value problem, while we
argue that a related model instead has an ill-posed initial value problem; in
the second case, we still prove the existence of solutions in analytic function
spaces. Finally we prove the existence of some periodic traveling waves.
