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.
Highlights
In the present paper we study the time evolution of a patch of temperature in R2 according to the modified surface quasi-geostrophic (SQG) equation, considered in recent years by different authors
We recall the basic equations of the α-patch model: let θ(x, t), x ∈ R2 be the solution of the equation
In this paper we will generalize the last result, for the estimate of the growth of the support of a temperature patch according to the α-patch model
Summary
In the present paper we study the time evolution of a patch of temperature in R2 according to the modified surface quasi-geostrophic (SQG) equation, considered in recent years by different authors (see e.g. [12] and the references therein). In the present paper we study the time evolution of a patch of temperature in R2 according to the modified surface quasi-geostrophic (SQG) equation, considered in recent years by different authors
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