Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global regular motions for compressible barotropic viscous fluids.
  Stability   We consider viscous compressible barotropic motions in a bounded domain
$\Omega \subset \mathbb{R}^3$ with the Dirichlet boundary conditions for
velocity. We assume the existence of some special sufficiently regular
solutions $v_s$ (velocity), $\varrho_s$ (density) of the problem. By the
special solutions we can choose spherically symmetric solutions. Let $v$,
$\varrho$ be a~solution to our problem. Then we are looking for differences
$u=v-v_s$, $\eta=\varrho-\varrho_s$. We prove existence of $u$, $\eta$ such
that $u,\eta\in L_\infty(kT,(k+1)T;H^2(\Omega))$, $u_t,\eta_t\in
L_\infty(kT,(k+1)T;H^1(\Omega))$, $u\in L_2(kT,(k+1)T;H^3(\Omega))$, $u_t\in
L_2(kT,(k+1)T;H^2(\Omega))$, where $T>0$ is fixed and $k \in \mathbb{N} \cup
\{0 \}$. Moreover, $u$, $\eta$ are sufficiently small in the above norms. This
also means that stability of the special solutions $v_s$, $\varrho_s$ is
proved. Finally, we proved existence of solutions such that $v=v_s+u$,
$\varrho=\varrho_s+\eta$.

1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an