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

Hui Li; Weiren Zhao

doi:10.1007/s00220-023-04671-3

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

Hui Li, Weiren Zhao

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-geostrophic equation with small viscosity ν around the quasi-steady state Θ _sin= - e^-^ν^tsin 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 cosy∂x(-Δ)-12θ re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.

Original language	English (US)
Pages (from-to)	1383-1415
Number of pages	33
Journal	Communications In Mathematical Physics
Volume	401
Issue number	2
DOIs	https://doi.org/10.1007/s00220-023-04671-3
State	Published - Jul 2023

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-023-04671-3

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title = "Metastability for the Dissipative Quasi-Geostrophic Equation and the Non-local Enhancement",

abstract = "In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-geostrophic equation with small viscosity ν around the quasi-steady state Θ sin= - e-νtsin 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 cosy∂x(-Δ)-12θ re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.",

author = "Hui Li and Weiren Zhao",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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N2 - In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-geostrophic equation with small viscosity ν around the quasi-steady state Θ sin= - e-νtsin 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 cosy∂x(-Δ)-12θ re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.

AB - In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-geostrophic equation with small viscosity ν around the quasi-steady state Θ sin= - e-νtsin 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 cosy∂x(-Δ)-12θ re-enhances the enhanced diffusion effect by the shear-diffusion mechanism.

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

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