On a class of three dimensional Navier-Stokes equations with bounded delay

Sandro M. Guzzo; Gabriela Planas

doi:10.3934/dcdsb.2011.16.225

Article Contents

2011, Volume 16, Issue 1: 225-238. Doi: 10.3934/dcdsb.2011.16.225

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On a class of three dimensional Navier-Stokes equations with bounded delay

Sandro M. Guzzo^1, and
Gabriela Planas^2,

1.
Universidade Estadual do Oeste do Paraná - UNIOESTE, Colegiado do curso de Matemática, Rua Universitária, 2069. Cx.P. 711, 85819-110 Cascavel, PR
2.
Departamento de Matemática, IMECC - UNICAMP, Rua Sergio Buarque de Holanda, 651, 13083-859 Campinas, SP

Received: May 31, 2010

Revised: August 31, 2010

Published: June 2011

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Abstract

In this paper we consider a three dimensional Navier-Stokes type equations with delay terms. We discuss the existence of weak and strong solutions and we study the asymptotic behavior of the strong solutions. Moreover, under suitable assumptions, we show the exponential stability of stationary solutions.

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Mathematics Subject Classification: Primary: 35Q35, 76D05; Secondary: 35B40.

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References

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