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Long Time Existence and Asymptotic Behavior of Solutions for the 2D Quasi-geostrophic Equation with Large Dispersive Forcing

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Abstract

We consider the initial value problem of the 2D dispersive quasi-geostrophic equation. We prove the long time existence of the solution for given initial data \(\theta _0 \in H^s(\mathbb {R}^2)\) with \(s>2\). Moreover, we show that the solution converges to the corresponding linear dispersive solution \(e^{-AtR_1}\theta _0\) when the size of dispersion parameter goes to infinity.

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Acknowledgements

The author would like to express his sincere gratitude to Professor Jun-ichi Segata and Professor Ryo Takada for many fruitful advices and continuous encouragement.

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  1. Graduate School of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan

    Mikihiro Fujii

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  1. Mikihiro Fujii
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Correspondence to Mikihiro Fujii.

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Fujii, M. Long Time Existence and Asymptotic Behavior of Solutions for the 2D Quasi-geostrophic Equation with Large Dispersive Forcing. J. Math. Fluid Mech. 23, 12 (2021). https://doi.org/10.1007/s00021-020-00540-4

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