三维Micropolar流体方程组弱解的正则性准则
Regularity Criteria of Weak Solutions to the 3D Micropolar Fluid Equations
DOI: 10.12677/AAM.2021.109318, PDF,   
作者: 何贝贝：浙江师范大学数学与计算机科学学院，浙江 金华
关键词: Micropolar流体方程组；Besov空间；弱解；正则性准则；Micropolar流体方程组；Besov空间；弱解；正则性准则
摘要: 本文给出了三维Micropolar流体方程组在Besov空间中弱解的一个正则性准则，证明了当方程组的弱解(u,w)满足,时，方程组(1.1)在(0,T]上是正则的。
Abstract: In this paper, we study the regularity criteria for the weak solutions of 3D Micropolar fluid equations (1.1) in Besov space. We get that the weak solution (u,w) is regular on (0,T] when it satisfies the conditions ,, where 0<γ<2.
文章引用：何贝贝. 三维Micropolar流体方程组弱解的正则性准则[J]. 应用数学进展, 2021, 10(9): 3039-3044. https://doi.org/10.12677/AAM.2021.109318

参考文献

[1] Heywood, J.G. (1980) The Navier-Stokes Equations: On the Existence, Regularity and Decay of Solutions. Indiana University Mathematics Journal, 29, 639-681. [Google Scholar] [CrossRef] 
[2] Caffarelli, L., Kohn, R. and Nirenberg, L. (1982) Partial Regularity of Suitable Weak Solutions of the Navier-Stokes Equations. Communications on Pure and Applied Mathematics, 35, 771-831. [Google Scholar] [CrossRef] 
[3] Cao, C. and Titi, E.S. (2008) Regularity Criteria for the Three-Dimensional Navier-Stokes Equations. Indiana University Mathematics Journal, 57, 2643-2661. [Google Scholar] [CrossRef] 
[4] Eringen, A.C. (1966) Theory of Micropolar Fluids. Journal of Mathematics and Mechanics, 16, 1-18. [Google Scholar] [CrossRef] 
[5] Dong, B.Q. and Zhang, W. (2010) On the Regularity Criterion for the Three-Dimensional Micropolar Flows in Besov Spaces. Nonlinear Analysis: Theory, Methods & Applications, 73, 2334-2341. [Google Scholar] [CrossRef] 
[6] Wang, Y.X. and Zhao, H.J. (2012) Logarithmically Improved Blow up Criterion for Smooths Solution to the 3D Micropolar Fluid Equations. Journal of Applied Mathematics, 10, 1-13. [Google Scholar] [CrossRef] 
[7] Zhang, H. (2014) Logarithmically Improved Regularity Criterion for the 3D Micropolar Fluid Equations. International Journal of Analysis, 10, 1-6. [Google Scholar] [CrossRef] 
[8] Gala, S. (2011) On Regularity Criteria for the Three-Dimensional Micropolar Fluid Equations in the Critical MorreyCampanato Space. Nonlinear Analysis: Real World Applications, 12, 2142-2150. [Google Scholar] [CrossRef] 
[9] Lions, P.L. (1998) Mathematical Topics in Fluid Mechanics. Oxford Lecture Series in Mathematics and Its Applications. Clarendon Press, Oxford.
[10] Yuan, B. (2010) Regularity of Weak Solutions to Magneto-Micropolar Fluid Equations. Acta Mathematica Scientia, 30, 1469-1480. [Google Scholar] [CrossRef] 

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