On Stokes' Problem
On Stokes' Problem
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关于斯托克斯问题
DOI：
10.1007/978-3-642-04068-9_28
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
R. Russo
中科院分区：
文献类型：
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作者：
R. Russo
本文研究了在有界Lipschitz区域和外Lipschitz区域上粘性流体动力学的Stokes问题。我们证明了这个问题在有界域上有唯一的非常弱解。就外部域而言，我们证明了存在一个非常弱的解决方案，使得在无穷远，与pk的斯托克斯多项式的程度为k，当且仅当数据满足一个适当的兼容性条件。特别是，我们得到了著名的斯托克斯悖论的流体力学非常弱的解决方案。我们利用这一结果证明了Navier-Stokes问题在有界和外部Lipschitz域中的一个很弱解的存在性。
We consider the Stokes problem of viscous hydrodynamics in bounded and exterior Lipschitz domains O of with boundary datum in. We show that this problem has a unique very weak solution in bounded domains. As far as exterior domains are concerned, we prove that a very weak solution exists such that at infinity, with pk a Stokes's polynomial of degree k, if and only if the data satisfy a suitable compatibility condition. In particular, we derive the well-known Stokes'paradox of hydrodynamics for very weak solutions. We use this results to prove the existence of a very weak solution to the Navier-Stokes problem in bounded and exterior Lipschitz domains of by requiring that the boundary datum belongs to.