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

  • *Corresponding author: Wenjun Liu

    *Corresponding author: Wenjun Liu 

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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  • 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.

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

    Citation:

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