Confinement of a hot temperature patch in the modified SQG model. (English) Zbl 1418.35344

Garra, Roberto

Discrete Contin. Dyn. Syst., Ser. B 24, No. 6, 2407-2416 (2019).

Summary: 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.

MSC:

35Q86	PDEs in connection with geophysics
76E20	Stability and instability of geophysical and astrophysical flows
37N10	Dynamical systems in fluid mechanics, oceanography and meteorology

Keywords:

modified surface quasi-geostrophic equation; confinement of temperature patch; active scalar flow