WIAS Preprint No. 2727, (2020)
On the spatially asymptotic structure of time-periodic solutions to the Navier--Stokes equations
- Eiter, Thomas
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.
- Probab. Surv., 149 (2021), pp. 3439--3451, DOI 10.1090/proc/15482 .