Global well-posedness of the three-dimensional viscous primitive equations with bounded delays

Zhenduo Fan; Wenjun Liu; Shengqian Chen

doi:10.3934/dcdsb.2022019

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2022, Volume 27, Issue 11: 6771-6796. Doi: 10.3934/dcdsb.2022019

This issue Previous Article Canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple Allee effect Next Article On the quasineutral limit for the compressible Euler-Poisson equations

Global well-posedness of the three-dimensional viscous primitive equations with bounded delays

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

^*Corresponding author: Wenjun Liu
^*Corresponding author: Wenjun Liu

Received: July 2021

Revised: November 2021

Early access: February 2022

Published: November 2022

This work was supported by the National Natural Science Foundation of China [grant numbers 11771216 and 11901306], the Key Research and Development Program of Jiangsu Province (Social Development) [grant number BE2019725], and the Natural Science Foundation of Jiangsu Province [grant number SBK2017043142]

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Abstract

The study of delay is one of the important problems in fluid mechanics. When we attempt to control the fluid in some sense, this delay may occur by applying a force that takes into account not only the current state of the system, but also the known history. In this paper, the three-dimensional viscous primitive equations with bounded delays are considered. We prove the existence of weak and strong solutions, and obtain the uniqueness of the strong solution. We also obtain the exponential decay behavior of the weak solutions and get some higher order estimates for strong solution. Under appropriate assumptions, we prove that the time-dependent weak solutions converge exponentially to the unique stationary solution.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76D03, 35B40.

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