Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2002-03-31
$L_q-L_r$-Estimates for Non-Stationary Stokes Equations in an Aperture DomainHelmut Abels (1) Universität Regensburg, Germany
This article deals with asymptotic estimates of strong solutions of Stokes equations in aperture domains. An aperture domain is a domain, which outside a bounded set is identical to two half spaces separated by a wall and connected inside the bounded set by one or more holes in the wall. It is known that the corresponding Stokes operator generates a bounded analytic semigroup in the closed subspace $J_q(\Omega)$ of divergence free vector fields of $L_q(\Omega)^n$. We deal with $L_q-L_r$-estimates for the semigroup, which are known for $\mathbb R^n$, the half space and exterior domains.
Keywords: Stokes equations, aperture domains, asymptotic behavior, asymptotic expansions
Abels Helmut: $L_q-L_r$-Estimates for Non-Stationary Stokes Equations in an Aperture Domain. Z. Anal. Anwend. 21 (2002), 159-178. doi: 10.4171/ZAA/1069