Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions
Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions
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具有混合边界条件的无限层中的广义斯托克斯求解方程
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
H. Abels
中科院分区：
文献类型：
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作者：
H. Abels
本文证明了无限层Ω0=ℝn-1×(-1，1)，n≥2中广义Stokes预解方程在Lq-∞空间1<；q<；∂Ω上滑移边界条件∂Ω+0=ℝn-1×{1}和下边界∂Ω-0=ℝn-1×{-1}上的唯一可解性.利用拉普拉斯预解方程的解算子和作用在边界上的Mikhlin乘子算子来表示Stokes系统的解算子。本文的结果是在L 2-空间中建立Beale[9]和Sylvester[22]所研究的自由边值问题的Lq理论的第一步。(2006 Wiley-VCH Verlag GmbH&Co.KGaA，Weinheim)
In this paper we prove unique solvability of the generalized Stokes resolvent equations in an infinite layer Ω0 = ℝn –1 × (–1, 1), n ≥ 2, in Lq ‐Sobolev spaces, 1 < q < ∞, with slip boundary condition of on the “upper boundary” ∂Ω+0 = ℝn –1 × {1} and non‐slip boundary condition on the “lower boundary” ∂Ω–0 = ℝn –1 × {–1}. The solution operator to the Stokes system will be expressed with the aid of the solution operators of the Laplace resolvent equation and a Mikhlin multiplier operator acting on the boundary. The present result is the first step to establish an Lq ‐theory for the free boundary value problem studied by Beale [9] and Sylvester [22] in L 2‐spaces. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)