# American Institute of Mathematical Sciences

June  2019, 24(6): 2407-2416. doi: 10.3934/dcdsb.2018258

## Confinement of a hot temperature patch in the modified SQG model

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

Received  July 2017 Revised  February 2018 Published  October 2018

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.

Citation: Roberto Garra. Confinement of a hot temperature patch in the modified SQG model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2407-2416. doi: 10.3934/dcdsb.2018258
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