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September  2010, 14(2): 655-673. doi: 10.3934/dcdsb.2010.14.655

Three dimensional system of globally modified Navier-Stokes equations with infinite delays

Pedro Marín-Rubio 1, , Antonio M. Márquez-Durán 1, and  José Real 2,

1. 

Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080–Sevilla, Spain
2. 

Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received  September 2009 Revised  March 2010 Published  June 2010

Existence and uniqueness of solution for a globally modified version of Navier-Stokes equations containing infinite delay terms are established. Moreover, we also analyze the stationary problem and, under suitable additional conditions, we obtain global exponential decay of the solutions of the evolutionary problem to the stationary solution.
Keywords: Globally Modified Navier-Stokes Equations; infinite delays..
Mathematics Subject Classification: Primary: 35K55, 35Q30, 34D23, 34K2.
Citation: Pedro Marín-Rubio, Antonio M. Márquez-Durán, José Real. Three dimensional system of globally modified Navier-Stokes equations with infinite delays. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 655-673. doi: 10.3934/dcdsb.2010.14.655
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