Decomposition of Vector-Valued Divergence Free Sobolev Functions and Shape Optimization for Stationary Navier–Stokes Equations
Decomposition of Vector-Valued Divergence Free Sobolev Functions and Shape Optimization for Stationary Navier–Stokes Equations
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DOI：
10.1080/03605300801895258
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发表时间：
2005-10
影响因子：
1.9
通讯作者：
GengshengBB Wang;Donghui Yang
中科院分区：
文献类型：
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作者：
GengshengBB Wang;Donghui Yang
建立了Rn，n-≥1中具有自由散度的向量值Ω函数的无散度分拆.证明了对Rn，n=2，3中的任一𝒞类区域Ω，该空间与其在H1(Soblev)n-范数中的完备性是相同的.我们还将证明A.E.在Ω}中，其中D是使Ω⊂⊂D有界的Lipschitz域，这些结果与𝒞类区域的性质一起被用来解决定常N-S方程形状优化理论中的一个存在性问题。
We establish a divergence free partition for vector-valued Sobolev functions with free divergence in R n , n ≥ 1. We prove that for any domain Ω of class 𝒞 in R n ,n = 2,3, the space and the space , which is the completion of in the H 1(Ω) n -norm, are identical. We will also prove that a.e. in Ω}, where D is a bounded Lipschitz domain such that Ω ⊂ ⊂ D. These results, together with properties for domains of class 𝒞, are used to solve an existence problem in the shape optimization theory of the stationary Navier–Stokes equations.