胡薇,刘瑞宽

• 1:西南石油大学理学院

摘要(Abstract)：

讨论了具有时滞项和非线性阻尼项的三维微极流方程强解的全局适定性。运用Galerkin近似方法，在非线性阻尼项指标满足一定条件下，证明了该问题强解的存在性和唯一性。

关键词(KeyWords)： 微极流;时滞;阻尼项;Galerkin方法;强解;全局适定性

Abstract:

Keywords:

基金项目(Foundation): 四川省自然科学基金面上项目(2022NSFC0529);; 南充市西南石油大学本校科技战略合作专项(23XNSYJG005)资助

作者(Author): 胡薇,刘瑞宽

参考文献(References)：

• [1] ERINGEN A C.Theory of micropolar ??uids [J].Journal of Mathematics and Mechanics,1966,16:1-18.
• [2] LUKASZEWICZ G.On nonstationary ??ows of asymmetric ??uids [J].Accademia Nazionale delle Scienze detta dei XL Rendiconti Serie V Memorie di Matematica e Applicazioni,1988,12:83-97.
• [3] LUKASZEWICZ G.On the existence,uniqueness and asymptotic properties for solutions of ??ows of asymmetric ??uids [J].Accademia Nazionale delle Scienze detta dei XL Rendiconti Serie V Memorie di Matematica e Applicazioni,1989,13(1):105-120.
• [4] LUKASZEWICZ G.Long time behavior of 2D micropolar ??uid ??ows [J].Mathematical and Computer Modelling,2001,34(5):487-509.
• [5] LUKASZEWICZ G.Asymptotic behavior of micropolar ??uid ??ows [J].International Journal of Engineering Science,2003,41(3):259-269.
• [6] JIU Q S,LIU J T,WU J H,et al.On the initial and boundary value problem for 2D micropolar equations with only angular velocity dissipation [J].Journal of Applied Mathematics and Physics,2017,68(5):1-24.
• [7] YAMAGUCHI N.Existence of global strong solution to the micropolar ??uid system in a bounded domain [J].Mathematical Methods in the Applied Sciences,2005,28(13):1507-1526.
• [8] ZHUAN Y.Global existence of strong solution to the 3D micropolar equations with a damping term [J].Applied Mathematics Letters,2018,83:188-193.
• [9] YANG X J,LIU H,SUN C F.Global attractors of the 3D micropolar equations with damping term [J].Mathematical Foundations of Computing,2021,4(2):117-130.
• [10] CARABALLO T,REAL J.Navier-Stokes equations with delays [J].Proceedings of the Royal Society of London Series A:Mathematical,Physical and Engineering Sciences,2001,457(2014):2441-2453.
• [11] CARABALLO T,REAL J.Asymptotic behaviour of two-dimensional Navier-Stokes equations with delays[J].Proceedings of the Royal Society of London.Series A:Mathematical,Physical and Engineering Sciences,2003,459(2040):3181-3194.
• [12] CARABALLO T,REAL J.Attractors for two-dimensional Navier-Stokes models with delays [J].Journal of Differential Equations,2004,205(2):271-297.
• [13] LU R,GUO C X,YANG X G,et al.Dynamics for three dimensional generalized Navier-Stokes quations with delay [J].Journal of Partial Di??erential Equations,2022,35(2):123-147.
• [14] SUN W L.Micropolar ??uid ??ows with delay on 2D unbounded domains [J].Journal of Applied Analysis and Computation,2018,8(1):356-378.
• [15] SUN W L,LIU G W.Pullback attractor for the 2D micropolar fluid flows with delay on un-bounded domains [J].Bulletin of the Malaysian Mathematical Sciences Society,2019,42(5):2807-2833.
• [16] EVANS L C.Partial differential equations [M].New York:American mathematical society,2022.