Some regularity results for a double time-delayed 2D-Navier-Stokes model

Julia García-Luengo; Pedro Marín-Rubio; Gabriela Planas

doi:10.3934/dcdsb.2018337

Article Contents

2019, Volume 24, Issue 8: 3929-3946. Doi: 10.3934/dcdsb.2018337

This issue Previous Article Multiobjective model predictive control for stabilizing cost criteria Next Article Persistence in non-autonomous quasimonotone parabolic partial functional differential equations with delay

Some regularity results for a double time-delayed 2D-Navier-Stokes model

1.
Departamento de Matemática Aplicada a las TIC, Universidad Politécnica de Madrid, C/ Nikola Tesla s/n, 28031, Madrid, Spain
2.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, C/ Tarfia s/n, 41012, Sevilla, Spain
3.
Departamento de Matemática, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, 13083-859 Campinas, SP, Brazil

Dedicated to Professor Peter E. Kloeden on occasion of his Seventieth Birthday

Received: May 2018

Revised: September 2018

Early access: January 2019

Published: August 2019

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Abstract

In this paper we analyze some regularity properties of a double time-delayed 2D-Navier-Stokes model, that includes not only a delay force but also a delay in the convective term. The interesting feature of the model -from the mathematical point of view- is that being in dimension two, it behaves similarly as a 3D-model without delay, and extra conditions in order to have uniqueness were required for well-posedness. This model was previously studied in several papers, being the existence of attractor in the $ L^2 $-framework obtained by the authors [Discrete Contin. Dyn. Syst. 34 (2014), 4085-4105]. Here regularization properties of the solutions and existence of (regular) attractors for several associated dynamical systems are established. Moreover, relationships among these objects are also provided.

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Mathematics Subject Classification: Primary: 35Q30, 35Q35, 35B65, 35B41, 37L30.

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References

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