  We study the (in)stability around the dynamical gap solution of the $U(N)$
Chern-Simons gauge theory with fundamental fermions (massless or massive)
coupled in $D=3$ at large $N$. Explicit analyses on both the Auxiliary-Field
(AF) and the Cornwall-Jackiw-Tomboulis (CJT) effective potentials are given. In
both approaches we manage to analytically identify the saddle-point instability
around the gap solution. We also give a comparison with the QCD-like theories.
This study can help understanding the scale symmetry breaking picture of this
theory.
