Spatial Pointwise Behavior of Time-Periodic Navier–Stokes Flow Induced by Oscillation of a Moving Obstacle

Toshiaki Hishida
Additional contact information
Toshiaki Hishida: Nagoya University, Graduate School of Mathematics

A chapter in Collected Papers in Honor of Yoshihiro Shibata, 2022, pp 369-394 from Springer

Abstract: Abstract We study the spatial decay of time-periodic Navier–Stokes flow at the rate |x| −1 with/without wake structure in 3D exterior domains when a rigid body moves periodically in time. In this regime the existence of time-periodic solutions was established first in the 2006 paper by Galdi and Silvestre, however, with little information about spatial behavior at infinity so that uniqueness of solutions was not available. This latter issue has been addressed by Galdi, who has recently succeeded in construction of a unique time-periodic solution with spatial behavior mentioned above if translational and angular velocities of the body fulfill, besides smallness and regularity, either of the following assumptions: (i) translation or rotation is absent; (ii) both velocities are parallel to the same constant vector. This paper shows the existence of a unique time-periodic Navier–Stokes flow in the small with values in the weak-L3 space and then deduces the desired pointwise decay of the solution under some condition on the rigid motion of the body, that covers the cases (i), (ii) mentioned above.

Keywords: Navier-Stokes flow; time-periodic solution; exterior domain; spatial behavior; rigid motion (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-19252-4_16

Ordering information: This item can be ordered from
http://www.springer.com/9783031192524

DOI: 10.1007/978-3-031-19252-4_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().