Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

被引：8

作者：

Eiter, Thomas ^{[1
]}

Kyed, Mads ^{[2
,3
]}

机构：

[1] Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany

[2] Flensburg Univ Appl Sci, Kanzleistr 91-93, D-24943 Flensburg, Germany

[3] Waseda Univ, Fac Sci & Engn, Tokyo, Japan

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2021年 / 23卷 / 01期

关键词：

Navier-Stokes; Oseen flow; Time-periodic solutions; Rotating obstacles; 35Q30; 35B10; 76D05; 76D07; 76U05;

D O I：

10.1007/s00021-021-00556-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

引用

页数：23

共 55 条

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