TY - JOUR

T1 - On a generalized resolvent estimate for the Stokes system with Robin boundary condition

AU - Shibata, Yoshihiro

AU - Shimada, Rieko

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007/4

Y1 - 2007/4

N2 - We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L q framework (1 < q < ∞) in a domain of Rn (n ≧ 2) that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: v · u = 0 and au + β(T(u, p)v -(T(u, p)u, v)v) = h on the boundary of the domain with α, β ≧ 0 and α + β= 1, where u denotes a velocity vector, p 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 the non-slip one when α = 1, respectively.

AB - We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L q framework (1 < q < ∞) in a domain of Rn (n ≧ 2) that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: v · u = 0 and au + β(T(u, p)v -(T(u, p)u, v)v) = h on the boundary of the domain with α, β ≧ 0 and α + β= 1, where u denotes a velocity vector, p 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 the non-slip one when α = 1, respectively.

KW - Resolvent estimate

KW - Robin boundary condition

KW - Stokes system

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U2 - 10.2969/jmsj/05920469

DO - 10.2969/jmsj/05920469

M3 - Article

AN - SCOPUS:34547487815

VL - 59

SP - 469

EP - 519

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -