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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月6日

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  • Thomas Eiter,
  • Ana Leonor Silvestre

摘要

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.