Three dimensional system of globally modified Navier-Stokesequations with infinite delays

Pedro Marín-Rubio; Antonio M. Márquez-Durán; José Real

doi:10.3934/dcdsb.2010.14.655

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2010, Volume 14, Issue 2: 655-673. Doi: 10.3934/dcdsb.2010.14.655

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

1.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080–Sevilla
2.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received: August 31, 2009

Revised: February 28, 2010

Published: August 2010

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Abstract

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, 34K20.

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