WIAS Preprint No. 2791, (2020)

Spatial decay of the vorticity field of time-periodic viscous flow past a body


  • Eiter, Thomas
    ORCID: 0000-0002-7807-1349
  • Galdi, Giovanni P.
    ORCID: 0000-0003-3812-9400

2010 Mathematics Subject Classification

  • 35Q30 35B10 76D05 35E05


  • Navier-Stokes, time-periodic solutions, vorticity field, fundamental solution, asymptotic behavior




We study the asymptotic spatial behavior of the vorticity field associated to a time-periodic Navier-Stokes flow past a body in the class of weak solutions satisfying a Serrin-like condition. We show that outside the wake region the vorticity field decays pointwise at an exponential rate, uniformly in time. Moreover, decomposing it into its time-average over a period and a so-called purely periodic part, we prove that inside the wake region, the time-average has the same algebraic decay as that known for the associated steady-state problem, whereas the purely periodic part decays even faster, uniformly in time. This implies, in particular, that ``sufficiently far'' from the body, the time-periodic vorticity field behaves like the vorticity field of the corresponding steady-state problem.

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