Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness and long-time dynamics for a higher order
  Quasi-Geostrophic type equation   In this paper we study a higher order viscous quasi-geostrophic type
equation. This equation was derived in [11] as the limit dynamics of a
singularly perturbed Navier-Stokes-Korteweg system with Coriolis force, when
the Mach, Rossby and Weber numbers go to zero at the same rate. The scope of
the present paper is twofold. First of all, we investigate well-posedness of
such a model on the whole space $\R^2$: we prove that it is well-posed in $H^s$
for any $s\geq3$, globally in time. Interestingly enough, we show that this
equation owns two levels of energy estimates, for which one gets existence and
uniqueness of weak solutions with different regularities (namely, $H^3$ and
$H^4$ regularities); this fact can be viewed as a remainder of the so called
BD-entropy structure of the original system. In the second part of the paper we
investigate the long-time behaviour of these solutions. We show that they
converge to the solution of the corresponding linear parabolic type equation,
with same initial datum and external force. Our proof is based on dispersive
estimates both for the solutions to the linear and non-linear problems.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg