JournalszaaVol. 21, No. 1pp. 159–178

LqLrL_q-L_r-Estimates for Non-Stationary Stokes Equations in an Aperture Domain

  • Helmut Abels

    Universität Regensburg, Germany
$L_q-L_r$-Estimates for Non-Stationary Stokes Equations in an Aperture Domain cover
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Abstract

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 Jq(Ω)J_q(\Omega) of divergence free vector fields of Lq(Ω)nL_q(\Omega)^n. We deal with LqLrL_q-L_r-estimates for the semigroup, which are known for Rn\mathbb R^n, the half space and exterior domains.

Cite this article

Helmut Abels, LqLrL_q-L_r-Estimates for Non-Stationary Stokes Equations in an Aperture Domain. Z. Anal. Anwend. 21 (2002), no. 1, pp. 159–178

DOI 10.4171/ZAA/1069