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2003 On a resolvent estimate for the Stokes system with Neumann boundary condition
Yoshihiro Shibata, Senjo Shimizu
Differential Integral Equations 16(4): 385-426 (2003).


We obtain the $L_p$ estimate of solutions to the resolvent problem for Stokes system with Neumann type boundary condition in a bounded or exterior domain in $\mathbb R^n$. The result has been obtained by Grubb and Solonnikov [7, 8, 9, 10] by the systematic use of theory of pseudo-differential operators. In this paper, we give an essentially different proof from [7, 8, 9, 10]. The point of our proof is to use the space $W^{-1}_p$ in order to handle with the equation $\nabla\cdot u = g$ in the half-space model problem as well as in the whole space one. Our result is an extension of the paper by Farwig and Sohr [5] about the Dirichlet zero condition case to the Neumann boundary condition case.


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Yoshihiro Shibata. Senjo Shimizu. "On a resolvent estimate for the Stokes system with Neumann boundary condition." Differential Integral Equations 16 (4) 385 - 426, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1054.35056
MathSciNet: MR1972873

Primary: 35Q30
Secondary: 35B45 , 47F05 , 76D07

Rights: Copyright © 2003 Khayyam Publishing, Inc.


Vol.16 • No. 4 • 2003
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