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Metastability for the Dissipative Quasi-Geostrophic Equation and the Non-local Enhancement

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Abstract

In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-geostrophic equation with small viscosity \(\nu \) around the quasi-steady state \(\Theta _{\sin }=-e^{-\nu t}\sin y\). We proved the linear enhanced dissipation and obtained the dissipation rate. Moreover, the new non-local enhancement phenomenon was discovered and discussed. Precisely we showed that the non-local term \(\cos y\partial _x(-\Delta )^{-\frac{1}{2}}\theta \) re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.

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Authors and Affiliations

  1. Department of Mathematics, New York University Abu Dhabi, Saadiyat Island, P.O. Box 129188, Abu Dhabi, United Arab Emirates

    Hui Li & Weiren Zhao

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Hui Li

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  1. Hui Li
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  2. Weiren Zhao
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Correspondence to Weiren Zhao.

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Li, H., Zhao, W. Metastability for the Dissipative Quasi-Geostrophic Equation and the Non-local Enhancement. Commun. Math. Phys. 401, 1383–1415 (2023). https://doi.org/10.1007/s00220-023-04671-3

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