Confinement of a hot temperature patch in the modified SQG model

Roberto Garra

doi:10.3934/dcdsb.2018258

Article Contents

2019, Volume 24, Issue 6: 2407-2416. Doi: 10.3934/dcdsb.2018258

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Confinement of a hot temperature patch in the modified SQG model

Roberto Garra^,

Department of Statistical Sciences, Sapienza University of Rome, P.le Aldo Moro, 5, 00185, Rome, Ital

Received: June 30, 2017

Revised: January 31, 2018

Early access: October 2018

Published: June 2019

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Abstract

In this paper we study the time evolution of a temperature patch in $\mathbb{R}^2$ according to the modified Surface Quasi-Geostrophic (SQG) patch equation. In particular we give a temporal estimate on the growth of the support, providing a rigorous proof of the confinement of a hot patch of temperature in absence of external forcing, under the quasi-geostrophic approximation.

Keywords:

Modified Surface Quasi-Geostrophic equation,
confinement of temperature patch,
active scalar flow.

Mathematics Subject Classification: Primary: 35Q86, 76E20; Secondary: 37N10.

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