WIAS Preprint No. 2727, (2020)

On the spatially asymptotic structure of time-periodic solutions to the Navier--Stokes equations


  • Eiter, Thomas
    ORCID: 0000-0002-7807-1349

2010 Mathematics Subject Classification

  • 35Q30 35B10 35C20 76D05 35E05


  • Navier--Stokes, time-periodic solutions, asymptotic expansion, Oseen system, fundamental solution




The asymptotic behavior of weak time-periodic solutions to the Navier--Stokes equations with a drift term in the three-dimensional whole space is investigated. The velocity field is decomposed into a time-independent and a remaining part, and separate asymptotic expansions are derived for both parts and their gradients. One observes that the behavior at spatial infinity is determined by the corresponding Oseen fundamental solutions.

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