A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions
A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions
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DOI：
10.3934/dcdss.2015.8.1079
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
T. Caraballo;Xiaoying Han
中科院分区：
文献类型：
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作者：
T. Caraballo;Xiaoying Han
在这篇综述论文中，我们回顾了与Navier-Stokes模型相关的几个方面，当一些遗传特性（常数，分布或可变延迟，记忆等）出现在公式中时。首先，一些结果的存在性和/或唯一性的解决方案。其次，利用李雅普诺夫函数理论、Razumikhin-Lyapunov技术以及构造适当的李雅普诺夫泛函，研究了稳态解的局部稳定性分析。一个Gronwall引理延迟方程也被利用，提供一些稳定性结果。最后，我们还包括一些评论的整体渐近分析的模型，以及一些开放的问题和未来的研究方向。
In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics (constant, distributed or variable delay, memory, etc) appear in the formulation. First some results concerning existence and/or uniqueness of solutions are established. Next the local stability analysis of steady-state solutions is studied by using the theory of Lyapunov functions, the Razumikhin-Lyapunov technique and also by constructing appropriate Lyapunov functionals. A Gronwall-like lemma for delay equations is also exploited to provide some stability results. In the end we also include some comments concerning the global asymptotic analysis of the model, as well as some open questions and future lines for research.