Asymptotic structure for solutions of the Navier--Stokes equations

Tian Ma; Shouhong Wang

doi:10.3934/dcds.2004.11.189

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2004, Volume 11, Issue 1: 189-204. Doi: 10.3934/dcds.2004.11.189

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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: January 31, 2003

Revised: October 31, 2003

Published: December 2003

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Abstract

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.

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Mathematics Subject Classification: 34D, 35Q35, 58F, 76, 86A10.

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