# American Institute of Mathematical Sciences

April  2020, 19(4): 1931-1948. doi: 10.3934/cpaa.2020085

## Longtime behavior for 3D Navier-Stokes equations with constant delays

 1 Department of Mathematics and Statistics, University of Wyoming, Laramie 82071 USA 2 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Sevilla, SPAIN, 41012

Dedicated to Tomás Caraballo on his 60th birthday

Received  June 2019 Revised  October 2019 Published  January 2020

Fund Project: The first author was partially supported by Simons Foundation grant 582264. The second author was partially supported by grant PGC2018-096540-I00.

This paper investigates the longtime behavior of delayed 3D Navier-Stokes equations in terms of attractors. The study will strongly rely on the investigation of the linearized Navier-Stokes system, and the relationship between the discrete dynamical flow for the linearized system and the continuous flow associated to the original system. Assuming the viscosity to be sufficiently large, there exists a unique attractor for the delayed 3D Navier-Stokes equations. Moreover, the attractor reduces to a singleton set.

Citation: Hakima Bessaih, María J. Garrido-Atienza. Longtime behavior for 3D Navier-Stokes equations with constant delays. Communications on Pure & Applied Analysis, 2020, 19 (4) : 1931-1948. doi: 10.3934/cpaa.2020085
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