Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On asymptotically almost periodic solutions to the Navier-Stokes
  equations in hyperbolic manifolds   In this paper we extend a recent work \cite{HuyXuan2020} to study the forward
asymptotically almost periodic (AAP-) mild solution of Navier-Stokes equation
on the real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$ with dimension $d
\geq 2$. Using the dispertive and smoothing estimates for Stokes equation
\cite{Pi} we invoke the Massera-type principle to prove the existence and
uniqueness of the AAP- mild solution for the Stokes equation in
$L^p(\Gamma(TM)))$ space with $p>d$. We then establish the existence and
uniqueness of the small AAP- mild solutions of the Navier-Stokes equation by
using the fixed point argument. The asymptotic behaviour (exponential decay and
stability) of these small solutions are also related. Our results extend also
\cite{FaTa2013} for the forward asymptotic mild solution of the Navier-Stokes
equation on the curved background.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat