| Abstract: |
| We consider 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 {\rm div}\, u=g \text{ in }\Omega \
&u|_{z=1}= h, \quad u|_{z=0}, \quad u|_{t=0}= u|_{t=2\pi},
\end{align*}
where the data $f, g, h$ are also time periodic and smooth with bounded support for simplicity and present results about existence and the asymptotic behavior of the solutions in space. |
|