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Author: Eiter, Thomas × Subject: fundamental solution ×

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    On the spatially asymptotic structure of time-periodic solutions to the Navier--Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Eiter, Thomas
    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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    Spatial decay of the vorticity field of time-periodic viscous flow past a body
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Eiter, Thomas; Galdi, Giovanni P.
    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.