Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness and scattering of inhomogeneous cubic-quintic NLS   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 $\mathbf L = x \times (-i\nabla)$.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg