American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Asymptotic behavior of the compressible viscous potential fluid: Renormalization group approach
  • DCDS Home
  • This Issue
  • Next Article
    Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems
January  2004, 11(1): 189-204. doi: 10.3934/dcds.2004.11.189

Asymptotic structure for solutions of the Navier--Stokes equations

Tian Ma 1, and  Shouhong Wang 2,

1. 

Department of Mathematics, Sichuan University, Chengdu
2. 

Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  February 2003 Revised  November 2003 Published  April 2004

We study in this article the large time asymptotic structural stability and structural evolution in the physical space for the solutions of the 2-D Navier-Stokes equations with the periodic boundary conditions. Both the Hamiltonian and block structural stabilities and structural evolutions are considered, and connections to the Lyapunov stability are also given.
Keywords: divergence-free vector fields, Navier-Stokes equations, Lyapunov stability., periodic boundary conditions, structural stability, block stability, Hamiltonian stability.
Mathematics Subject Classification: 34D, 35Q35, 58F, 76, 86A1.
Citation: Tian Ma, Shouhong Wang. Asymptotic structure for solutions of the Navier--Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 189-204. doi: 10.3934/dcds.2004.11.189
[1]

Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409
[2]

Jing Wang, Lining Tong. Stability of boundary layers for the inflow compressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2595-2613. doi: 10.3934/dcdsb.2012.17.2595
[3]

Jie Liao, Xiao-Ping Wang. Stability of an efficient Navier-Stokes solver with Navier boundary condition. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 153-171. doi: 10.3934/dcdsb.2012.17.153
[4]

Mehdi Badra, Fabien Caubet, Jérémi Dardé. Stability estimates for Navier-Stokes equations and application to inverse problems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2379-2407. doi: 10.3934/dcdsb.2016052
[5]

Bingkang Huang, Lusheng Wang, Qinghua Xiao. Global nonlinear stability of rarefaction waves for compressible Navier-Stokes equations with temperature and density dependent transport coefficients. Kinetic & Related Models, 2016, 9 (3) : 469-514. doi: 10.3934/krm.2016004
[6]

Yuming Qin, Lan Huang, Zhiyong Ma. Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1991-2012. doi: 10.3934/cpaa.2009.8.1991
[7]

Chuong V. Tran, Theodore G. Shepherd, Han-Ru Cho. Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 483-494. doi: 10.3934/dcdsb.2002.2.483
[8]

Yinnian He, Pengzhan Huang, Jian Li. H2-stability of some second order fully discrete schemes for the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2745-2780. doi: 10.3934/dcdsb.2018273
[9]

Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. Kinematical structural stability. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 529-536. doi: 10.3934/dcdss.2016010
[10]

Luis Barreira, Claudia Valls. Stability of nonautonomous equations and Lyapunov functions. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2631-2650. doi: 10.3934/dcds.2013.33.2631
[11]

Augusto Visintin. Weak structural stability of pseudo-monotone equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2763-2796. doi: 10.3934/dcds.2015.35.2763
[12]

Renjun Duan, Xiongfeng Yang. Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations. Communications on Pure & Applied Analysis, 2013, 12 (2) : 985-1014. doi: 10.3934/cpaa.2013.12.985
[13]

Roberto Triggiani. Stability enhancement of a 2-D linear Navier-Stokes channel flow by a 2-D, wall-normal boundary controller. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 279-314. doi: 10.3934/dcdsb.2007.8.279
[14]

Jifeng Chu, Meirong Zhang. Rotation numbers and Lyapunov stability of elliptic periodic solutions. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1071-1094. doi: 10.3934/dcds.2008.21.1071
[15]

M'hamed Kesri. Structural stability of optimal control problems. Communications on Pure & Applied Analysis, 2005, 4 (4) : 743-756. doi: 10.3934/cpaa.2005.4.743
[16]

Petr Kučera. The time-periodic solutions of the Navier-Stokes equations with mixed boundary conditions. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 325-337. doi: 10.3934/dcdss.2010.3.325
[17]

Feng Wang, José Ángel Cid, Mirosława Zima. Lyapunov stability for regular equations and applications to the Liebau phenomenon. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4657-4674. doi: 10.3934/dcds.2018204
[18]

Hantaek Bae. Solvability of the free boundary value problem of the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 769-801. doi: 10.3934/dcds.2011.29.769
[19]

Jean-Pierre Raymond. Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1537-1564. doi: 10.3934/dcdsb.2010.14.1537
[20]

Chérif Amrouche, Nour El Houda Seloula. $L^p$-theory for the Navier-Stokes equations with pressure boundary conditions. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1113-1137. doi: 10.3934/dcdss.2013.6.1113

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences