Communications in Mathematical Sciences

Volume 22 (2024)

Number 6

A note on enhanced dissipation of time-dependent shear flows

Pages: 1685 – 1700

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n6.a10

Authors

Daniel Coble (Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA)

Siming He (Department of Mathematics, University of South Carolina, Columbia, SC, USA)

Abstract

This paper explores the phenomena of enhanced dissipation in solutions to the passive scalar equations subject to time-dependent shear flows. The hypocoercivity functionals with carefully tuned time weights are applied in the analysis. We observe that as long as the critical points of the shear flow vary slowly, one can derive the sharp enhanced dissipation estimates, mirroring the ones obtained for the time-stationary case.

Keywords

enhanced dissipation, time-dependent shear flows

2010 Mathematics Subject Classification

35K10, 35Q35, 35Q92

The full text of this article is unavailable through your IP address: 172.17.0.1

Received 27 September 2023

Received revised 20 January 2024

Accepted 25 January 2024

Published 18 July 2024