Existence, Uniqueness and Asymptotic Behavior of Regular Time-Periodic Viscous Flow around a Moving Body

2020/03/15 by Giovanni P. Galdi, Galdi, Giovanni P.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.06913

openalex publication_date 2020/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show existence and uniqueness of regular time-periodic solutions to the Navier-Stokes problem in the exterior of a rigid body, \mathscr B, that moves by arbitrary (sufficiently smooth) time-periodic translational motion of the same period, provided the size of the data is suitably restricted. Moreover, we characterize the spatial asymptotic behavior of such solutions and prove, in particular, that if \mathscr B has a nonzero net motion identified by a constant velocity \mathbfξ (say), then the solution exhibit a wake-like behavior in the direction -\mathbfξ entirely analogous to that of a steady-state flow around a body that moves with velocity \mathbfξ.

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