  This paper concerns a free-boundary fluid-structure interaction problem for
plaque growth proposed by Yang et al. [J. Math. Biol., 72(4):973--996, 2016]
with additional viscoelastic effects, which was also investigated by the
authors [arXiv preprint: 2110.00042, 2021]. Compared to it, the problem is
posed in a cylindrical domain with ninety-degree contact angles, which brings
additional difficulties when we deal with the linearization of the system By a
reflection argument, we obtain the existence and uniqueness of strong solutions
to the model problems for the linear systems, which are then shown to be
well-posed in a cylindrical (annular) domain via a localization procedure.
Finally, we prove that the full nonlinear system admits a unique strong
solution locally with the aid of the contraction mapping principle.
