  In this paper we consider inhomogeneous cubic-quintic NLS in space dimension
$d = 3$: $$ iu_t = -\Delta u + K_1(x)|u|^2u + K_2(x)|u|^4u. $$ We study local
well-posedness, finite time blowup, and small data scattering and
non-scattering for the ICQNLS when $K_1, K_2 \in C^4(\mathbb R^3 \setminus
\{0\})$ satisfy growth condition $|\partial^j K_i(x)| \lesssim |x|^{b_i-j}\, (j
= 0, 1, 2, 3, 4)$ for some $b_i \ge 0$ and for $x \neq 0$. To this end we use
the Sobolev inequality for the functions $f \in H^n \,(n = 1, 2)$ such that
$\||\mathbf L|^\ell f\|_{H^n} < \infty \,(\ell = 1, 2)$, where $\mathbf L$ is
the angular momentum operator defined by $\mathbf L = x \times (-i\nabla)$.
