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13/03/2025
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Nguyen, N. H., Le, T. M. H., Nguyen, T. L., & Pham, N. G. (2025). Periodic solutions to the non-autonomous Oseen-Navier-Stokes equations in exterior domains. Journal of Water Resources & Environmental Engineering, 97, 13-19. https://dev.vojs.vn/index.php/jwree/article/view/6
Periodic solutions to the non-autonomous Oseen-Navier-Stokes equations in exterior domains
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Abstract
In this paper, we investigate the existence and uniqueness of periodic mild solutions to the non autonomous Oseen-Navier-Stokes equations (ONSE) in the exterior domain 3R of a rotating obstacle that is translating with a time-dependent velocity. Our method is based on the p q L L smoothness of the evolution family corresponding to linearized equations in combination with interpolation spaces and fixed-point theorems.
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Keywords
Evolution families, Periodic solutions, Oseen-Navier-Stokes equations, rotating and translating obstacle.
References
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T. Hishida (2020), Decay estimates of gradient of a generalized Oseen evolution operator arising from time-dependent rigid motions in exterior domains. Arch. Rational Mech. Anal. 238, 215–254.
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Thieu Huy Nguyen, T.K.O Tran (2024), Periodic Motions of the Non-autonomous Oseen-Navier-Stokes Flows Past a Moving Obstacle with Data in pL-Spaces, Vietnam J. Math. 52, 219-233.
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M. Yamazaki (2000), The Navier-Stokes equations in the weak-nL space with time-dependent external force, Math. Ann., 317, 635-675.
W. Borchers and T. Miyakawa (1995), On stability of exterior stationary Navier-Stokes flows, Acta Math, 174, 311-382.
Galdi, G.P. (2022), Navier–Stokes flow past a rigid body that moves by time-periodic motion. J. Math. Fluid Mech. 24, 30.
T. Hansel, A. Rhandi (2014), The Oseen–Navier–Stokes flow in the exterior of a rotating obstacle: the nonautonomous case. J. Reine Angew. Math., 1–26.
T. Hishida (2020), Decay estimates of gradient of a generalized Oseen evolution operator arising from time-dependent rigid motions in exterior domains. Arch. Rational Mech. Anal. 238, 215–254.
H. Komatsu (1981), A general interpolation theorem of Marcinkiewicz type, Tohoku Math. J. 33 (2), 383-393.
H. Kozono and M. Nakao (1996), Periodic solution of the Navier-Stokes equations in unbounded domains, Tohoku Math. J., 48, 33-50.
Thieu Huy Nguyen, T.K.O Tran (2024), Periodic Motions of the Non-autonomous Oseen-Navier-Stokes Flows Past a Moving Obstacle with Data in pL-Spaces, Vietnam J. Math. 52, 219-233.
J. Serrin (1959), A note on the existence of periodic solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 3, 120-122.
H. Tribel (1978), "Interpolation Theory, Function Spaces, Differential Operators", North-Holland, Amsterdam, New York, Oxford.
M. Yamazaki (2000), The Navier-Stokes equations in the weak-nL space with time-dependent external force, Math. Ann., 317, 635-675.