Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension Reduction of Compressible Fluid Models over Product Manifolds   In this paper we study the dimension reduction limits of the compressible
Navier--Stokes equations over product Riemannian manifolds
$\mathcal{O}_\epsilon \cong \mathcal{M} \times \epsilon\mathcal{F}$, such that
$\dim\,(\mathcal{M})=n$ and $\dim\,(\mathcal{F})=d$ are arbitrary. Using the
method of relative entropies, we establish the convergence of the suitable weak
solutions of the Navier--Stokes equations on $\mathcal{O}_\epsilon$ to the
classical solution of the limiting equations on $\mathcal{M}$ as $\epsilon
\rightarrow 0^+$, provided the latter exists. In addition, we also deduce the
vanishing viscosity limit. The limiting equations identified through our
analysis contain the weight function $A:\mathcal{M} \rightarrow \mathbb{R}^+$
as a parameter, where $A(x)$ = area of fibre $\mathcal{F}_x$. Our work is based
on and generalises the results in P. Bella, E. Feireisl, M. Lewicka and A.
Novotn\'{y}, A rigorous justification of the Euler and Navier--Stokes equations
with geometric effects, \textit{SIAM J. Math. Anal.}, \textbf{48} (2016),
3907--3930, and it contains as special cases the physical models of circular
nozzles, thin plate limits and finite-length longitudinal nozzles.

32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph