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Periodic and almost periodic motions of Navier–Stokes flows and their stability in a perturbed half-space

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Abstract

Consider the system of Navier–Stokes equations in a perturbed half-space. We study the existence and stability of periodic solutions and almost periodic solutions to this system. For the Stokes system we use \(L^p\text {-}L^q\) estimates in combination with interpolation spaces to show the existence of bounded (in time) mild solutions as well as the existence of periodic solutions. Moreover, the existence of almost periodic solutions is proved. Then the existence, uniqueness and stability of the periodic and almost periodic solutions to the Navier–Stokes system are proved by using fixed-point arguments and certain interpolation relations.

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Acknowledgements

We thank the Reviewer for his or her careful reading of the manuscript, especially for his/her suggestion on formulation of the problem on the whole line time-axis. His/her corrections and comments help to improve the paper. The work is financially supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.02\(-\)2021.04.

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  1. Faculty of Mathematics and Informatics, Hanoi University of Science and Technology, Khoa Toan - Tin, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

    Thi Ngoc Ha Vu & Thieu Huy Nguyen

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  1. Thi Ngoc Ha Vu
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  2. Thieu Huy Nguyen
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Correspondence to Thieu Huy Nguyen.

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Vu, T.N.H., Nguyen, T.H. Periodic and almost periodic motions of Navier–Stokes flows and their stability in a perturbed half-space. Anal.Math.Phys. 14, 28 (2024). https://doi.org/10.1007/s13324-024-00887-1

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