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 - A, 2009, 23 (3) : 765-784. doi: 10.3934/dcds.2009.23.765
[1]

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

[2]

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

[3]

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

[4]

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

[5]

Fritz Colonius, Paulo Régis C. Ruffino. Nonlinear Iwasawa decomposition of control flows. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 339-354. doi: 10.3934/dcds.2007.18.339

[6]

Alexandre I. Danilenko, Mariusz Lemańczyk. Spectral multiplicities for ergodic flows. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4271-4289. doi: 10.3934/dcds.2013.33.4271

[7]

Keonhee Lee, Ngoc-Thach Nguyen, Yinong Yang. Topological stability and spectral decomposition for homeomorphisms on noncompact spaces. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2487-2503. doi: 10.3934/dcds.2018103

[8]

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

[9]

Ramon Plaza, K. Zumbrun. An Evans function approach to spectral stability of small-amplitude shock profiles. Discrete & Continuous Dynamical Systems - A, 2004, 10 (4) : 885-924. doi: 10.3934/dcds.2004.10.885

[10]

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

[11]

T. Tachim Medjo, Louis Tcheugoue Tebou. Robust control problems in fluid flows. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 437-463. doi: 10.3934/dcds.2005.12.437

[12]

Kazuo Yamazaki. Global regularity of the two-dimensional magneto-micropolar fluid system with zero angular viscosity. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2193-2207. doi: 10.3934/dcds.2015.35.2193

[13]

Baoquan Yuan, Xiao Li. Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2167-2179. doi: 10.3934/dcdss.2016090

[14]

Jinbo Geng, Xiaochun Chen, Sadek Gala. On regularity criteria for the 3D magneto-micropolar fluid equations in the critical Morrey-Campanato space. Communications on Pure & Applied Analysis, 2011, 10 (2) : 583-592. doi: 10.3934/cpaa.2011.10.583

[15]

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 - A, 2008, 21 (1) : 1-20. doi: 10.3934/dcds.2008.21.1

[16]

Kazuhiro Kurata, Tatsuya Watanabe. A remark on asymptotic profiles of radial solutions with a vortex to a nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2006, 5 (3) : 597-610. doi: 10.3934/cpaa.2006.5.597

[17]

Ryo Ikehata, Marina Soga. Asymptotic profiles for a strongly damped plate equation with lower order perturbation. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1759-1780. doi: 10.3934/cpaa.2015.14.1759

[18]

Tohru Wakasa, Shoji Yotsutani. Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems. Communications on Pure & Applied Analysis, 2010, 9 (2) : 539-561. doi: 10.3934/cpaa.2010.9.539

[19]

Rafael Tiedra De Aldecoa. Spectral analysis of time changes of horocycle flows. Journal of Modern Dynamics, 2012, 6 (2) : 275-285. doi: 10.3934/jmd.2012.6.275

[20]

Evgenii S. Baranovskii. Steady flows of an Oldroyd fluid with threshold slip. Communications on Pure & Applied Analysis, 2019, 18 (2) : 735-750. doi: 10.3934/cpaa.2019036

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (28)

Other articles
by authors

[Back to Top]