Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness, stability and instability for the non-viscous
  Oldroyd-B model   In this paper we consider the 3-dimensional incompressible Oldroyd-B model.
First, we establish two results of the global existence for different kinds of
the coupling coefficient $k$. Then, we prove that the solutions $(u,\tau)$ are
globally steady when $k^m\rightarrow k>0$, though $(u,\tau)$ corresponds to
different decays for different kinds of $k>0~$. Finally, we show that the
energy of $u(t,x)$ will have a jump when $k\rightarrow 0$ in large time, which
implies a non-steady phenomenon. In a word, we find an interesting physical
phenomenon of \eqref{1} such that smaller coupling coefficient $k$ will have a
better impact for the energy dissipation of $(u,\tau)$, but $k$ can't be too
small to zero, or the dissipation will vanish instantly. While the damping term
$\tau$ and $\mathbb{D}u$ always bring the well impact for the energy
dissipation.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org