Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous justification of Taylor dispersion via center manifolds and
  hypocoercivity   Taylor diffusion (or dispersion) refers to a phenomenon discovered
experimentally by Taylor in the 1950s where a solute dropped into a pipe with a
background shear flow experiences diffusion at a rate proportional to $1/\nu$,
which is much faster than what would be produced by the static fluid if its
viscosity is $0 < \nu \ll 1$. This phenomenon is analyzed rigorously using the
linear PDE governing the evolution of the solute. It is shown that the solution
can be split into two pieces, an approximate solution and a remainder term. The
approximate solution is governed by an infinite-dimensional system of ODEs that
possesses a finite-dimensional center manifold, on which the dynamics
correspond to diffusion at a rate proportional to $1/\nu$. The remainder term
is shown to decay at a rate that is much faster than the leading order behavior
of the approximate solution. This is proven using a spectral decomposition in
Fourier space and a hypocoercive estimate to control the intermediate Fourier
modes.

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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th