Approximation of stationary statistical properties of the three dimensional autonomous planetary geostrophic equations of large-scale ocean circulation

Bo You; Chunxiang Zhao

doi:10.3934/dcdsb.2020057

Article Contents

2020, Volume 25, Issue 8: 3183-3198. Doi: 10.3934/dcdsb.2020057

This issue Previous Article Global attraction in a system of delay differential equations via compact and convex sets Next Article Exit problem for Ornstein-Uhlenbeck processes: A random walk approach

Approximation of stationary statistical properties of the three dimensional autonomous planetary geostrophic equations of large-scale ocean circulation

Bo You^1, , and
Chunxiang Zhao^2,

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
2.
Department of Mathematics, Nanjing University, Nanjing 210093, China

^* Corresponding author: Bo You
^* Corresponding author: Bo You

Received: May 2019

Revised: October 2019

Early access: February 2020

Published: August 2020

This work was supported by the National Science Foundation of China Grant (11401459, 11801427), the Natural Science Foundation of Shaanxi Province (2018JM1012) and the Fundamental Research Funds for the Central Universities (xjj2018088)

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Abstract

The main objective of this paper is to study the semi-implicit semi-discrete scheme in time of the three dimensional autonomous planetary geostrophic equations of large-scale ocean circulation. We prove the global attractor and stationary statistical properties of the semi-implicit semi-discrete scheme in time of the three dimensional autonomous planetary geostrophic equations of large-scale ocean circulation converge to those of the three dimensional autonomous planetary geostrophic equations of large-scale ocean circulation as the time step goes to zero.

Keywords:

Global attractor,
planetary geostrophic equations,
semi-implicit semi-discrete scheme in time,
stationary statistical property.

Mathematics Subject Classification: Primary: 35B40, 35B41, 37M25, 37N10, 65M12; Secondary: 35Q35.

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