Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local weak solutions to a Navier-Stokes-nonlinear-Schr\"odinger model of
  superfluidity   In a 1959 paper by Pitaevskii, a macroscopic model of superfluidity was
derived from first principles, to describe the interacting dynamics between the
superfluid and normal fluid phases of Helium-4. The model couples two of the
most fundamental PDEs in mathematics: the nonlinear Schr\"odinger equation
(NLS) and the Navier-Stokes equations (NSE). In this article, we show the local
existence of weak solutions to this system (in a smooth bounded domain in 3D),
by deriving the required a priori estimates. (We will also establish an energy
inequality obeyed by the weak solutions constructed in Kim's 1987 paper for the
incompressible, inhomogeneous NSE.) To the best of our knowledge, this is the
first rigorous mathematical analysis of a bidirectionally coupled system of the
NLS and NSE.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph