The normal form of the Navier-Stokes equations in suitable normed spaces
The normal form of the Navier-Stokes equations in suitable normed spaces
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适当赋范空间中纳维-斯托克斯方程的范式
DOI：
10.1016/j.anihpc.2008.09.003
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发表时间：
2009
影响因子：
1.9
通讯作者：
M. Ziane
中科院分区：
文献类型：
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作者：
C. Foias;L. Hoang;Eric Olson;M. Ziane
考虑周期区域Ω=[0，2 π] 3上的不可压Navier-Stokes方程的解.设R ∈ H1（Ω）3表示所有导致正则解的初始数据的集合。我们的主要结果是构造一个适当的Banach空间SA_∞，使得规范化映射W：R→SA_∞是连续的，并且使得Navier-Stokes方程的规范型在所有SA_∞中是适定的。我们还表明，SA的可被视为一个更大的Banach空间V的子集和扩展的Navier-Stokes方程，这是已知的具有整体解决方案，在V的适定性。
We consider solutions to the incompressible Navier–Stokes equations on the periodic domain Ω=[0,2π]3with potential body forces. Let R⊆H1(Ω)3denote the set of all initial data that lead to regular solutions. Our main result is to construct a suitable Banach space SA⋆such that the normalization map W:R→SA⋆is continuous, and such that the normal form of the Navier–Stokes equations is a well-posed system in all of SA⋆. We also show that SA⋆may be seen as a subset of a larger Banach space V⋆and that the extended Navier–Stokes equations, which are known to have global solutions, are well-posed in V⋆.
关于斯托克斯漂移
DOI：
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发表时间：
2010
期刊：
影响因子：
--
作者：
Kanbayashi;Hiroshi;Hirohisa Takenoshita;H.Okamoto
通讯作者：
H.Okamoto