Dissipativity of Fractional Navier-Stokes Equations with Variable Delay
Dissipativity of Fractional Navier-Stokes Equations with Variable Delay
复制标题
具有变时滞的分数阶纳维-斯托克斯方程的耗散性
DOI：
10.3390/math8112037
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发表时间：
2020-11-01
期刊：
影响因子：
2.4
通讯作者：
Nieto, Juan J.
中科院分区：
文献类型：
--
作者：
Liu, Lin F.;Nieto, Juan J.
利用经典Galerkin逼近、广义Aubin-Lions引理和Bellman-Gronwall引理研究了具有变时滞的二维分数阶Navier-Stokes方程的渐近性态。通过修正分数阶Halanay不等式和比较原理，研究了相应系统的耗散性，即得到了系统整体吸收集的存在性。此外，本文还改进了已有的一些结果.全局吸引集的存在性问题仍然是一个悬而未决的问题。
We use classical Galerkin approximations, the generalized Aubin-Lions Lemma as well as the Bellman-Gronwall Lemma to study the asymptotical behavior of a two-dimensional fractional Navier-Stokes equation with variable delay. By modifying the fractional Halanay inequality and the comparison principle, we investigate the dissipativity of the corresponding system, namely, we obtain the existence of global absorbing set. Besides, some available results are improved in this work. The existence of a global attracting set is still an open problem.