Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of global weak solutions to the kinetic Hookean dumbbell model
  for incompressible dilute polymeric fluids   We explore the existence of global weak solutions to the Hookean dumbbell
model, a system of nonlinear partial differential equations that arises from
the kinetic theory of dilute polymers, involving the unsteady incompressible
Navier--Stokes equations in a bounded domain in two or three space dimensions,
coupled to a Fokker--Planck-type parabolic equation. We prove the existence of
large-data global weak solutions in the case of two space dimensions.
Indirectly, our proof also rigorously demonstrates that, in two space
dimensions at least, the Oldroyd-B model is the macroscopic closure of the
Hookean dumbbell model. In three space dimensions, we prove the existence of
large-data global weak subsolutions to the model, which are weak solutions with
a defect measure, where the defect measure appearing in the Navier--Stokes
momentum equation is the divergence of a symmetric positive semidefinite
matrix-valued Radon measure.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas