  In this paper, a model for defects that was introduced in \cite{ZANV} is
studied. In the literature, the setting of most models for defects is the
function space SBV (special bounded variation functions) (see, e.g.,
\cite{ContiGarroni, GoldmanSerfaty}). However, this model regularizes the
director field to be in a Sobolev space by adding a second field to incorporate
the defect. A relaxation result in the case of fixed parameters is proven along
with some partial compactness results.
