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In this work we are interested in the well-posedness issues for the initialvalue problem associated with a higher order water wave model posed on ape\-rio\-dic domain $\mathbb{T}$. We derive some multilinear estimates and usethem in the contraction mapping argument to prove local well-posedness forinitial data in the periodic Sobolev space $H^s(\mathbb{T})$, $s\geq 1$. Withsome restriction on the parameters appeared in the model, we use the conservedquantity to obtain global well-posedness for given data with Sobolev regularity$s\geq 2$. Also, we use splitting argument to improve the global well-posednessresult in $H^s(\mathbb{T})$ for $1\leq s< 2$. Well-posedness result obtained inthis work is sharp in the sense that the flow-map that takes initial data tothe 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 solutioncorresponding to a smooth initial data may have arbitrarily large$H^s(\mathbb{T})$ norm, with $s<1$, for arbitrarily short time.

On the well-posedness, ill-posedness and norm-inflation for a higher order water wave model on a periodic domain