Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and equilibration of global weak solutions to Hookean-type
  bead-spring chain models for dilute polymers   We show the existence of global-in-time weak solutions to a general class of
coupled Hookean-type bead-spring chain models that arise from the kinetic
theory of dilute solutions of polymeric liquids with noninteracting polymer
chains. The class of models involves the unsteady incompressible Navier-Stokes
equations in a bounded domain in two or three space dimensions for the velocity
and the pressure of the fluid, with an elastic extra-stress tensor appearing on
the right-hand side in the momentum equation. The extra-stress tensor stems
from the random movement of the polymer chains and is defined by the Kramers
expression through the associated probability density function that satisfies a
Fokker-Planck-type parabolic equation, a crucial feature of which is the
presence of a center-of-mass diffusion term. We require no structural
assumptions on the drag term in the Fokker-Planck equation; in particular, the
drag term need not be corotational. With a square-integrable and
divergence-free initial velocity datum for the Navier-Stokes equation and a
nonnegative initial probability density function for the Fokker-Planck
equation, which has finite relative entropy with respect to the Maxwellian of
the model, we prove the existence of a global-in-time weak solution to the
coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the
absence of a body force, the weak solution decays exponentially in time to the
equilibrium solution, at a rate that is independent of the choice of the
initial datum and of the centre-of-mass diffusion coefficient.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin