Global in time L^p‐estimates for the instationary Stokes and Navier–Stokes flow through an aperture

Article type: Research Article

Authors: Fröhlich, Andreas

Affiliations: Department of Mathematics, TU Darmstadt, Schlossgartenstr. 7, D‐64289 Darmstadt, Germany E‐mail: [email protected]‐darmstadt.de

Abstract: Using a characterisation of maximal Lp‐regularity by ℛ‐bounded operator families we prove global in time estimates in $L^{p}({\mathbb{R}}_{+};L^{q}(\varOmega))$, 1<p,q<∞, for solutions of the instationary Stokes system in an aperture domain $\varOmega\subset{\mathbb{R}} ^{n}$, n≥3, with $\curpartial\varOmega\in C^{1,1}.$ The results are applied to obtain new global in time estimates for weak solutions of the Navier–Stokes equations with nonvanishing flux through the aperture.

Journal: Asymptotic Analysis, vol. 33, no. 3-4, pp. 321-335, 2003