Electron. J. Differential Equations, Vol. 2017 (2017), No. 290, pp. 1-6.

Improved lifespan of solutions to an inviscid surface quasi-geostrophic model

Zhihong Wen

This article consider the two-dimensional (2D) inviscid surface quasi-geostrophic (SQG) model. By studying the decay estimate of the operator $e^{\mathcal{R}_1^{2}t}$, we obtain an improved lifespan of the solutions to the corresponding model. More precisely, if the initial data is of size $\epsilon$, then the lifespan satisfies $T_{\epsilon}\simeq\epsilon^{-4/3}$, which improves the result obtained via hyperbolic methods.

Submitted November 10, 2016. Published November 21, 2017.
Math Subject Classifications: 35B35, 35Q35, 76B03.
Key Words: Surface quasi-geostrophic equation; lifespan; decay estimate.

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Zhihong Wen
Department of Mathematics and Statistics
Jiangsu Normal University
101 Shanghai Road
Xuzhou 221116, Jiangsu, China
email: wenzhihong1989@163.com

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