Time-period flow of a viscous liquid past a body

TL;DR

This paper investigates time-periodic solutions to the Navier-Stokes equations for viscous flow past a moving body, establishing estimates and proving existence of solutions using linearization and contraction mapping.

Contribution

It introduces a novel approach to analyze time-periodic viscous flows past a body by linearizing with the time-periodic Oseen equations and proving existence of solutions.

Findings

Established a priori Lp estimates for the linearized system.

Proved existence of time-periodic solutions to the Navier-Stokes equations.

Applied contraction mapping principle to nonlinear problem.

Abstract

Time-periodic solutions to the Navier-Stokes equations that govern the flow of a viscous liquid past a three-dimensional body moving with a time-periodic velocity are investigated. The net motion of the body over a full time-period is assumed to be non-zero. In this case the appropriate linearization of the system is constituted by the time-periodic Oseen equations in a three-dimensional exterior domain. A priori Lp estimates are established for this linearization. Based on these estimates, existence of a solution to the fully non-linear Navier-Stokes problem is obtained by the contraction mapping principle.