Representation formulas and far-field behavior of time-periodic incompressible viscous flow around a translating rigid body

Abstract

This paper is concerned with integral representations and asymptotic expansions of solutions to the time-periodic incompressible Navier–Stokes equations for fluid flow in the exterior of a rigid body that moves with constant velocity. Using the time-periodic Oseen fundamental solution, we derive representation formulas for solutions with suitable regularity. From these formulas, the decomposition of the velocity component of the fundamental solution into steady-state and purely periodic parts and their detailed decay rate in space, we deduce complete information on the asymptotic structure of the velocity and pressure fields.