Fourier Mass Lower Bounds for Batchelor‐Regime Passive Scalars

Communications on Pure and Applied Mathematics 2026 Open access

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Authors: William Cooperman, Keefer Rowan
DOI: 10.1002/cpa.70030
Cited by: 0
References: 40

Abstract

ABSTRACT Batchelor predicted that a passive scalar with diffusivity , advected by a smooth fluid velocity, should typically have Fourier mass distributed as for . For a broad class of velocity fields, we give a quantitative lower bound for a version of this prediction summed over constant width annuli in Fourier space. This improves on previously known results, which require the prediction to be summed over the whole ball.

Fields of Study & Subjects

Fluid Dynamics and Turbulent Flows Advanced Harmonic Analysis Research Navier-Stokes equation solutions

Publication details

Journal / source
Communications on Pure and Applied Mathematics
Volume
79
Issue
6
Pages
1449–1466
Publication date
16 January 2026
Language
EN