WIAS Preprint No. 3091, (2024)

Representation formulas and far-field behavior of time-periodic flow past a body


  • Eiter, Thomas
    ORCID: 0000-0002-7807-1349
  • Silvestre, Ana Leonor
    ORCID: 0000-0001-5972-3033

2020 Mathematics Subject Classification

  • 35Q30 76D05 76D07 35B10 35A08 35C15 35C20


  • Time-periodic Navier--Stokes flows, exterior domains, time-periodic Oseen fundamental solution, integral representation, asymptotic expansion




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.

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