Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary conditions and polymeric drag reduction for the Navier-Stokes
  equations   Reducing wall drag in turbulent pipe and channel flows is an issue of great
practical importance. In engineering applications, end-functionalized polymer
chains are often employed as agents to reduce drag. These are polymers which
are floating in the solvent and attach (either by adsorption or through
irreversible chemical binding) at one of their chain ends to the substrate
(wall). We propose a PDE model to study this setup in the simple setting where
the solvent is a viscous incompressible Navier-Stokes fluid occupying the bulk
of a smooth domain $\Omega\subset \mathbb{R}^d$, and the wall-grafted polymer
is in the so-called mushroom regime (inter-polymer spacing on the order of the
typical polymer length). The microscopic description of the polymer enters into
the macroscopic description of the fluid motion through a dynamical boundary
condition on the wall-tangential stress of the fluid, something akin to (but
distinct from) a history-dependent slip-length. We establish global
well-posedness of strong solutions in two-spatial dimensions and prove that the
inviscid limit to the strong Euler solution holds with a rate. Moreover, the
wall-friction factor $\langle f\rangle$ and the global energy dissipation
$\langle \varepsilon\rangle$ vanish inversely proportional to the Reynolds
number $Re$. This scaling corresponds to Poiseuille's law for the friction
factor $\langle f\rangle \sim1/ Re$ for laminar flow and thereby quantifies
drag reduction in our setting. These results are in stark contrast to those
available for physical boundaries without polymer additives modeled by, e.g.,
no-slip conditions, where no such results are generally known even in
two-dimensions.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex