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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 and Continuous Dynamical Systems, 2004, 11 (1) : 189-204. doi: 10.3934/dcds.2004.11.189
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