On the large time dynamics of a rapidly rotating convection model at infinite Prandtl number

Yanqiu Guo; Jing Tian

doi:10.3934/dcdss.2025059

Article Contents

2025, Volume 18, Issue 12: 3896-3916. Doi: 10.3934/dcdss.2025059

This issue Previous Article The exact limits of all order derivatives of the global smooth solution of a general Korteweg-de Vries-Burgers equation Next Article Generalized dichotomies via time rescaling

On the large time dynamics of a rapidly rotating convection model at infinite Prandtl number

Yanqiu Guo^1, , and
Jing Tian^2,

1.
Department of Mathematics and Statistics, Florida International University, Miami, FL 33331
2.
Department of Mathematics, Towson University, Towson, MD 21252

^*Corresponding author: Yanqiu Guo
^*Corresponding author: Yanqiu Guo

Received: March 2024

Revised: April 2025

Early access: April 27, 2025

Published online: April 27, 2025

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Abstract

This study focuses on the asymptotic behavior of a three-dimensional rapidly rotating convection model, when momentum diffusivity significantly surpasses thermal diffusivity at the infinite Prandtl number. We prove the existence of a global attractor and establish the backward uniqueness of solutions for this model. The main challenge in analyzing this model arises from the fluid domain being three-dimensional, while the diffusion is limited to the horizontal direction.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35K55.

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References

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