Unique solvability for the density-dependent incompressible Navier-Stokes-Korteweg system
Unique solvability for the density-dependent incompressible Navier-Stokes-Korteweg system
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密度相关不可压缩 Navier-Stokes-Korteweg 系统的独特可解性
DOI：
10.1016/j.jmaa.2017.03.071
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发表时间：
2017
影响因子：
1.3
通讯作者：
Wang Teng
中科院分区：
文献类型：
--
作者：
Wang Teng
这篇文章是一个贡献的频谱理论的所谓最终积极的运营商，即运营商T这可能不是积极的，但其权力T n成为积极的足够大的n。虽然这种算子的谱理论在有限维中得到了很好的理解，但无限维的情况在文献中受到的关注要少得多。我们表明，几个明智的概念“最终的积极性”可以定义在无限维的设置，并在有限维的情况下，这些概念一般不一致。然后，我们证明了各种典型的Perron-Frobenius型的结果：我们表明，一个最终正的运营商的谱半径包含在频谱中，我们给出了充分条件的频谱半径是一个本征值承认一个积极的本征向量，我们表明，周边谱的最终正运营商是一个循环集在相当一般的假设。我们所有的结果制定的Banach格上的运营商，他们中的许多人不施加任何紧性假设的运营商。
This article is a contribution to the spectral theory of so-called eventually positive operators, ie operators T which may not be positive but whose powers T n become positive for large enough n. While the spectral theory of such operators is well understood in finite dimensions, the infinite dimensional case has received much less attention in the literature. We show that several sensible notions of “eventual positivity” can be defined in the infinite dimensional setting, and in contrast to the finite dimensional case those notions do not in general coincide. We then prove a variety of typical Perron–Frobenius type results: we show that the spectral radius of an eventually positive operator is contained in the spectrum; we give sufficient conditions for the spectral radius to be an eigenvalue admitting a positive eigenvector; and we show that the peripheral spectrum of an eventually positive operator is a cyclic set under quite general assumptions. All our results are formulated for operators on Banach lattices, and many of them do not impose any compactness assumptions on the operator.