In this paper we consider the heat equation u s ⌬ u in an unbounded domain t N Ž . ⍀;R with a partly Dirichlet condition u x, t s 0 and a partly Neumann condition u s u p on the boundary, where p ) 1 and is the exterior unit normal on the boundary. It is shown that for a sectorial domain in R 2 and
✦ LIBER ✦
On a resolvent estimate of the Stokes equation with Neumann–Dirichlet-type boundary condition on an infinite layer
✍ Scribed by Takayuki Abe
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 339 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.483
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✦ Synopsis
Abstract
This paper is concerned with the standard Lp estimate of solutions to the resolvent problem for the Stokes operator on an infinite layer with ‘Neumann–Dirichlet‐type’ boundary condition. Copyright © 2004 John Wiley & Sons, Ltd.
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## Abstract In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fluid flow. We show standard resolvent estimates in the __L~q