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On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain

✍ Scribed by Rieko Shimada

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 328 KB
Volume: 30
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.777

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✦ Synopsis

Abstract

We obtain the L~p~–L~q~ maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ℝ^n^ (n⩾2). The Robin condition consists of two conditions: v ⋅ u=0 and α__u__+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β⩾0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd.

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On the Lp–Lq maximal regularity for the

On the Lp–Lq maximal regularity for the linear thermoelastic plate equation in a bounded domain

✍ Yuka Naito 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 261 KB

## Abstract This paper is concerned with the thermoelastic plate equations in a domain Ω: subject to the boundary condition: __u__|=__D__~ν~__u__|=θ|=0 and initial condition: (__u, u__~__t__~, θ)|~__t__=0~=(__u__~0~, __v__~0~, θ~0~). Here, Ω is a bounded domain in ℝ^__n__^(__n__≧2). We assume tha