Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note about existence for a class of viscous fluid problems   In this work the existence of weak solutions for a class of non-Newtonian
viscous fluid problems is analyzed. The problem is modeled by the steady case
of the generalized Navier-Stokes equations, where the exponent $q$ that
characterizes the flow depends on the space variable: $q=q(\mathbf{x})$. For
the associated boundary-value problem we show that, in some situations, the
log-H\"older continuity condition on $q$ can be dropped and the result of the
existence of weak solutions still remain valid for any variable exponent
$q\geq\alpha>\frac{2N}{N+2}$, where $\alpha=\mathrm{ess}\inf q$.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org