  In this paper, we establish the well-posedness in energy space for the
quintic energy critical wave inside a cylindrical convex domain
$\Omega\subset\mathbb{R}^3$ with smooth boundary $\partial\Omega\neq\emptyset$.
The key tools to prove local well-posedness are the dispersive estimates
obtained in \cite{L,L1,L3} and the Strichartz estimates in \cite{L2}. We point
out that our result on the local and global existence of the solution to the
wave equation in the cylindrical domain setting interpolates between that of in
Euclidean space $\mathbb{R}^3$ (see \cite{MG}) and in any bounded domains in
$\mathbb{R}^3$ (see \cite{BLP}). Moreover, the result of the Strichartz
estimates in our setting is strong enough when combined with the arguments in
\cite{BLP,SS2} so that we can extend local to global well-posedness.
