November  2008, 21(4): 1245-1258. doi: 10.3934/dcds.2008.21.1245

Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

1. 

Departamento de Matemática, ICMC-USP, CP 668, São Carlos-SP, 13560-970

2. 

Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo - Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos-SP, Brazil

Received  May 2007 Revised  January 2008 Published  May 2008

We consider the two-dimensional Navier-Stokes equations with a time-delayed convective term and a forcing term which contains some hereditary features. Some results on existence and uniqueness of solutions are established. We discuss the asymptotic behaviour of solutions and we also show the exponential stability of stationary solutions.
Citation: Gabriela Planas, Eduardo Hernández. Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1245-1258. doi: 10.3934/dcds.2008.21.1245
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