Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global weak solutions to the Navier-Stokes-Vlasov equations   In this paper, the system of particles coupled with fluid is considered. The
particles are described by a Vlasov equation, and the fluid is governed by a
forced Navier-Stokes equations. The interaction with fluid phase governed by
Navier-Stokes equations is taken into account through a source term. The
resulting system, namely Navier-Stokes-Vlasov equations, is shown to have
global weak solutions in three spatial dimensions, and to have a unique global
solution in two spatial dimensions.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph