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

Gabriela Planas; Eduardo Hernández

doi:10.3934/dcds.2008.21.1245

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2008, Volume 21, Issue 4: 1245-1258. Doi: 10.3934/dcds.2008.21.1245

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

Gabriela Planas^1, and
Eduardo Hernández^2,

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

Received: May 2007

Revised: January 2008

Published: October 2008

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Abstract

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.

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Mathematics Subject Classification: 35Q35, 35Q30, 35B40.

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