Periodic Motions of the Non-autonomous Oseen–Navier–Stokes Flows Past a Moving Obstacle with Data in Lp-Spaces

In this paper, we study the time-periodic mild solutions to the non-autonomous Oseen–Navier–Stokes equations (ONSE). We prove the existence and polynomial stability of such solutions to ONSE in the exterior domain Ω ⊂ ℝ 3 of a rigid body, D = ℝ 3 ∖ Ω , moving by time periodic motion of given period...

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Bibliographic Details
Published in:Vietnam journal of mathematics 2024-03, Vol.52 (1), p.219-233
Main Authors: Nguyen, Thieu Huy, Tran, Thi Kim Oanh
Format: Article
Language:English
Subjects:
Existence theorems
Fixed points (mathematics)
Fluid flow
Mathematical analysis
Mathematics
Mathematics and Statistics
Moving obstacles
Navier-Stokes equations
Original Article
Polynomials
Rigid structures
Smoothness
Stability
Stokes flow
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Summary:In this paper, we study the time-periodic mild solutions to the non-autonomous Oseen–Navier–Stokes equations (ONSE). We prove the existence and polynomial stability of such solutions to ONSE in the exterior domain Ω ⊂ ℝ 3 of a rigid body, D = ℝ 3 ∖ Ω , moving by time periodic motion of given period T , when the data belong to L p -space and are sufficiently small. Our method is based on the L p − L q smoothness of the evolution family corresponding to linearized equations in combination with ergodic theory and fixed-point theorems to obtain the result on existence and stability of T -periodic solutions under the actions of T -periodic external forces.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-022-00599-8