  In this work we are interested in the well-posedness issues for the initial
value problem associated with a higher order water wave model posed on a
pe\-rio\-dic domain $\mathbb{T}$. We derive some multilinear estimates and use
them in the contraction mapping argument to prove local well-posedness for
initial data in the periodic Sobolev space $H^s(\mathbb{T})$, $s\geq 1$. With
some restriction on the parameters appeared in the model, we use the conserved
quantity to obtain global well-posedness for given data with Sobolev regularity
$s\geq 2$. Also, we use splitting argument to improve the global well-posedness
result in $H^s(\mathbb{T})$ for $1\leq s< 2$. Well-posedness result obtained in
this work is sharp in the sense that the flow-map that takes initial data to
the solution cannot to be continuous for given data in $H^s(\mathbb{T})$, $s<
1$. Finally, we prove a norm-inflation result by showing that the solution
corresponding to a smooth initial data may have arbitrarily large
$H^s(\mathbb{T})$ norm, with $s<1$, for arbitrarily short time.
