# American Institute of Mathematical Sciences

July  2009, 23(3): 765-784. doi: 10.3934/dcds.2009.23.765

## Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows

 1 School of Mathematical Sciences, Anhui University, Hefei,Anhui 230039, China 2 School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom

Received  June 2007 Revised  August 2008 Published  November 2008

This paper deals with asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows in the whole space $R^2$. Based on the spectral decomposition of linearized micropolar fluid flows, the sharp algebraic time decay estimates of the micropolar fluid flows in $L_2$ and $L_\infty$ norms are obtained.
Citation: Bo-Qing Dong, Zhi-Min Chen. Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 765-784. doi: 10.3934/dcds.2009.23.765
 [1] Woochul Jung, Ngocthach Nguyen, Yinong Yang. Spectral decomposition for rescaling expansive flows with rescaled shadowing. Discrete & Continuous Dynamical Systems, 2020, 40 (4) : 2267-2283. doi: 10.3934/dcds.2020113 [2] Haibo Cui, Junpei Gao, Lei Yao. Asymptotic behavior of the one-dimensional compressible micropolar fluid model. Electronic Research Archive, 2021, 29 (2) : 2063-2075. doi: 10.3934/era.2020105 [3] Wenlong Sun, Jiaqi Cheng, Xiaoying Han. Random attractors for 2D stochastic micropolar fluid flows on unbounded domains. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 693-716. doi: 10.3934/dcdsb.2020189 [4] Wenlong Sun. The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay. Electronic Research Archive, 2020, 28 (3) : 1343-1356. doi: 10.3934/era.2020071 [5] Kazuo Yamazaki. Large deviation principle for the micropolar, magneto-micropolar fluid systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 913-938. doi: 10.3934/dcdsb.2018048 [6] Hiroshi Inoue, Kei Matsuura, Mitsuharu Ôtani. Strong solutions of magneto-micropolar fluid equation. Conference Publications, 2003, 2003 (Special) : 439-448. doi: 10.3934/proc.2003.2003.439 [7] Fritz Colonius, Paulo Régis C. Ruffino. Nonlinear Iwasawa decomposition of control flows. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 339-354. doi: 10.3934/dcds.2007.18.339 [8] Alexandre I. Danilenko, Mariusz Lemańczyk. Spectral multiplicities for ergodic flows. Discrete & Continuous Dynamical Systems, 2013, 33 (9) : 4271-4289. doi: 10.3934/dcds.2013.33.4271 [9] R. H.W. Hoppe, William G. Litvinov. Problems on electrorheological fluid flows. Communications on Pure & Applied Analysis, 2004, 3 (4) : 809-848. doi: 10.3934/cpaa.2004.3.809 [10] Keonhee Lee, Ngoc-Thach Nguyen, Yinong Yang. Topological stability and spectral decomposition for homeomorphisms on noncompact spaces. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2487-2503. doi: 10.3934/dcds.2018103 [11] Ramon Plaza, K. Zumbrun. An Evans function approach to spectral stability of small-amplitude shock profiles. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 885-924. doi: 10.3934/dcds.2004.10.885 [12] Zhi-Ying Sun, Lan Huang, Xin-Guang Yang. Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry. Electronic Research Archive, 2020, 28 (2) : 861-878. doi: 10.3934/era.2020045 [13] Haibo Cui, Haiyan Yin. Stability of the composite wave for the inflow problem on the micropolar fluid model. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1265-1292. doi: 10.3934/cpaa.2017062 [14] Cung The Anh, Vu Manh Toi. Local exact controllability to trajectories of the magneto-micropolar fluid equations. Evolution Equations & Control Theory, 2017, 6 (3) : 357-379. doi: 10.3934/eect.2017019 [15] Xin Zhong. Singularity formation to the nonhomogeneous magneto-micropolar fluid equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (12) : 6339-6357. doi: 10.3934/dcdsb.2021021 [16] Charles Amorim, Miguel Loayza, Marko A. Rojas-Medar. The nonstationary flows of micropolar fluids with thermal convection: An iterative approach. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2509-2535. doi: 10.3934/dcdsb.2020193 [17] Víctor Ayala, Adriano Da Silva, Philippe Jouan. Jordan decomposition and the recurrent set of flows of automorphisms. Discrete & Continuous Dynamical Systems, 2021, 41 (4) : 1543-1559. doi: 10.3934/dcds.2020330 [18] Alison M. Melo, Leandro B. Morgado, Paulo R. Ruffino. Decomposition of stochastic flows generated by Stratonovich SDEs with jumps. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3209-3218. doi: 10.3934/dcdsb.2016094 [19] T. Tachim Medjo, Louis Tcheugoue Tebou. Robust control problems in fluid flows. Discrete & Continuous Dynamical Systems, 2005, 12 (3) : 437-463. doi: 10.3934/dcds.2005.12.437 [20] Linda J. S. Allen, B. M. Bolker, Yuan Lou, A. L. Nevai. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete & Continuous Dynamical Systems, 2008, 21 (1) : 1-20. doi: 10.3934/dcds.2008.21.1

2020 Impact Factor: 1.392