Article citationsMore>>

Caraballo, T. and Han, X. (2015) A Survey on Navier-Stokes Models with Delays: Existence, Uniqueness and Asymptotic Behavior of Solutions. Discrete and Continuous Dynamical Systems—S, 8, 1079-1101.
https://doi.org/10.3934/dcdss.2015.8.1079

has been cited by the following article:

• TITLE: The Stability of a Class of Non-Newtonian Micropolar Fluid Equations with Unbounded Delays

  AUTHORS: Wanjia Liu, Luyan Yi

  KEYWORDS: Non-Newtonian Micropolar Fluid, Unbounded Delays, Weak (Strong) Solutions, Stationary Solution, Asymptotic (Polynomial) Stability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.6, June 11, 2026

  ABSTRACT: We address the stability of stationary solutions to a class of 2D non-newtonian micropolar fluid equations, when the external force contains hereditary characteristics involving unbounded delays. Specifically, when the delay function is continuous with respect to time, the stability of the weak solution with respect to the non-trivial stationary solution is established by the definition of Lyapunov stability, and the asymptotic stability of the weak solution with respect to the trivial stationary solution is established by the method of constructing Lyapunov functional; when the delay function is only continuous with respect to time, the stability of the strong solution with respect to the non-trivial stationary solution is established by using Razumikhin technique; finally, the proportional time delay is introduced to establish the polynomial stability of the weak solution with respect to the trivial stationary solution.