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Polynomial mixing under a certain stationary Euler flow

Crippa, Gianluca and Lucà, Renato and Schulze, Christian. (2019) Polynomial mixing under a certain stationary Euler flow. Physica D: Nonlinear Phenomena, 394. pp. 44-55.

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Official URL: https://edoc.unibas.ch/74297/

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Abstract

We study the mixing properties of a scalar ρ on the unit disk advected by a certain incompressible velocity field u, which is a stationary radial solution of the Euler equation. The scalar ρ solves the continuity equation with the velocity field u and we can measure the degree of "mixedness" of ρ with two different scales commonly used in this setting, namely the geometric and the functional mixing scale. We develop a physical space approach welladapted to the quantitative analysis of the decay in time of the geometric mixing scale, which turns out to be polynomial for a large class of initial data. This extends previous results for the functional mixing scale, based on the explicit expression for the solution in Fourier variable, results that are also partially recovered by our approach.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca and Schulze, Christian and Lucà, Renato
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0167-2789
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:13 Jan 2020 11:19
Deposited On:13 Jan 2020 11:19

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