Separation of time-scales in drift-diffusion equations on ℝ2
File(s)
Working paper
Author(s)
Coti Zelati, Michele
Dolce, Michele
Type
Working Paper
Abstract
We deal with the problem of separation of time-scales and filamentation in a
linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The
passive scalar considered is stirred by an incompressible flow with radial
symmetry. We identify a time-scale, much faster than the diffusive one, at
which mixing happens along the streamlines, as a result of the interaction
between transport and diffusion. This effect is also known as enhanced
dissipation. For power-law circular flows, this time-scale only depends on the
behavior of the flow at the origin. The proofs are based on an adaptation of a
hypocoercivity scheme and yield a linear semigroup estimate in a suitable
weighted $L^2$-based space.
linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The
passive scalar considered is stirred by an incompressible flow with radial
symmetry. We identify a time-scale, much faster than the diffusive one, at
which mixing happens along the streamlines, as a result of the interaction
between transport and diffusion. This effect is also known as enhanced
dissipation. For power-law circular flows, this time-scale only depends on the
behavior of the flow at the origin. The proofs are based on an adaptation of a
hypocoercivity scheme and yield a linear semigroup estimate in a suitable
weighted $L^2$-based space.
Date Issued
2019-07-09
Date Acceptance
2019-07-01
Citation
Journal de Mathematiques Pures et Appliquees, 2019
ISSN
0021-7824
Publisher
Elsevier
Journal / Book Title
Journal de Mathematiques Pures et Appliquees
Copyright Statement
© 2019 The Author(s).
Identifier
http://arxiv.org/abs/1907.04012v1
Subjects
math.AP
math.AP
Notes
14 pages, 1 figure
Publication Status
Published