Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations

Susan FRIEDLANDER, Chun Kit Anthony SUEN

Research output: Contribution to journalArticlespeer-review

Abstract

We investigate the properties of an abstract family of advection diffusion equations in the context of the fractional Laplacian. Two independent diffusion parameters enter the system, one via the constitutive law for the drift velocity and one as the prefactor of the fractional Laplacian. We obtain existence and convergence results in certain parameter regimes and limits. We study the long time behaviour of solutions to the general problem and prove the existence of a unique global attractor. We apply the results to two particular active scalar equations arising in geophysical fluid dynamics, namely the surface quasigeostrophic equation and the magnetogeostrophic equation. Copyright © 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.
Original languageEnglish
Pages (from-to)1431–1485
JournalArchive for Rational Mechanics and Analysis
Volume240
Issue number3
Early online date25 Mar 2021
DOIs
Publication statusPublished - Jun 2021

Citation

Friedlander, S., & Suen, A. (2021). Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations. Archive for Rational Mechanics and Analysis, 240(3), 1431–1485. doi: 10.1007/s00205-021-01638-3

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