WIAS Preprint No. 2727, (2020)
On the spatially asymptotic structure of time-periodic solutions to the Navier--Stokes equations
Authors
- Eiter, Thomas
ORCID: 0000-0002-7807-1349
2010 Mathematics Subject Classification
- 35Q30 35B10 35C20 76D05 35E05
Keywords
- Navier--Stokes, time-periodic solutions, asymptotic expansion, Oseen system, fundamental solution
DOI
Abstract
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.
Appeared in
- Probab. Surv., 149 (2021), pp. 3439--3451, DOI 10.1090/proc/15482 .
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