Long time localization of modified surface quasi-geostrophic equations

Guido Cavallaro; Roberto Garra; Carlo Marchioro

doi:10.3934/dcdsb.2020336

Article Contents

2021, Volume 26, Issue 9: 5135-5148. Doi: 10.3934/dcdsb.2020336

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Long time localization of modified surface quasi-geostrophic equations

1.
Sapienza Università di Roma, Dipartimento di Matematica, Piazzale Aldo Moro 2, 00185 Roma, Italy
2.
Sapienza Università di Roma, Dipartimento di Scienze Statistiche, Piazzale Aldo Moro 2, 00185 Roma, Italy
3.
International Research Center M&MOCS, Università di L'Aquila, Italy

^* Corresponding author: Guido Cavallaro
^* Corresponding author: Guido Cavallaro

Received: March 31, 2020

Early access: November 2020

Published: September 2021

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Abstract

We discuss the time evolution of a two-dimensional active scalar flow, which extends some properties valid for a two-dimensional incompressible nonviscous fluid. In particular we study some characteristics of the dynamics when the field is initially concentrated in $ N $ small disjoint regions, and we discuss the conservation in time of this localization property. We discuss also how long this localization persists, showing that in some cases this happens for quite long times.

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Mathematics Subject Classification: Primary: 76B47, 76M23; Secondary: 37C10, 86A99.

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