Affiliation:
1. Department of Mathematics Imperial College London London UK
2. Institut Fourier Université Grenoble Alpes, CNRS Grenoble France
Abstract
AbstractWe consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity , which is assumed to be small, and the wave number in the streamwise direction, which can take arbitrary values. Under generic assumptions on the shear velocity , we obtain optimal decay estimates for large times, both in the enhanced dissipation regime and in the Taylor dispersion regime . Our results can be deduced from resolvent estimates using a quantitative version of the Gearhart–Prüss theorem, or can be established more directly via the hypocoercivity method. Both approaches are explored in the present example, and their relative efficiency is compared.
Funder
Agence Nationale de la Recherche
Cited by
1 articles.
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