| Contents |
| We consider solutions to the
time periodic Stokes problem in a layer $\Omega = \mathbb{R}^2\times (0,1)\ni x=(y,z)$:
\begin{align*}
&u_t - \Delta u + \nabla p = f, \quad \operatorname{div} u=g \text{ in }\Omega \\
&u|_{z=1}= 0, \quad u|_{z=0}, \quad u|_{t=0}= u|_{t=2\pi},
\end{align*}
where the data $f, g$ are also time periodic and smooth with bounded support for simplicity.
Starting from solutions with $u \in L^2(L^2_\beta)$, $p \in L^2(L^2_\beta)$, where
$L^2_\beta(\Omega)$ is a weighted $L^2$-space with polynomial weight at infinity, we
derive the main asymptotic terms of $u, p$ as $|y|$ tends
to infinity. |
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