The Asymptotic Properties of the Solution to the Stokes Problem in Domains That Are Layer-Like at Infinity

The Asymptotic Properties of the Solution to the Stokes Problem in Domains That Are Layer-Like at Infinity
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无穷远层状域中斯托克斯问题解的渐近性质

DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
K. Pileckas
K. Pileckas
中科院分区：
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文献类型：
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作者：
S. Nazarov;K. Pileckas

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抽象的。给出了球外与三维层重合的区域中Stokes问题解的渐近公式 ${\bbb R}^2\x(0，1)$。分离的渐近项在横向和纵向上的性质不同。为了证明渐近展开式的正确性，我们使用了降维的方法以及解的各种加权范数的估计。
Abstract. Asymptotic formulae are derived for solutions to the Stokes problem in domains which, outside a ball, coincide with the three-dimensional layer $ {\Bbb R}^2 \times (0,1) $. The properties of detached asymptotic terms differ in the transversal and longitudinal directions. In order to justify the asymptotic expansions the procedure of dimension reduction is employed together with estimates for miscellaneous weighted norms of the solutions.