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3D Navier–Stokes–Voigt equations with damping and double delays on unbounded domains: Well-posedness, pullback attractors, and limit measures

Part of: Incompressible viscous fluids Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  18 March 2025

Zhengwang Tao ,
Dandan Yang  and
Yunfei Lv
Zhengwang Tao
Affiliation:
School of Mathematical Sciences, Tiangong University, No. 399 Binshui West Road, Xiqing District, Tianjin, 300387, China ([email protected])
Dandan Yang
Affiliation:
School of Mathematical Sciences, Tianjin Normal University, No. 393 Binshui West Road, Xiqing District, Tianjin, 300387, China ([email protected])
Yunfei Lv*
Affiliation:
School of Mathematical Sciences, Tiangong University, Tianjin, China ([email protected]) (corresponding author)
*
*Corresponding author.
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Abstract

This article is dedicated to investigating limit behaviours of invariant measures with respect to delay and system parameters of 3D Navier–Stokes–Voigt equations. Firstly, the well-posedness of such a system is obtained on arbitrary open sets that satisfy the Poincaré inequality, and then a unique minimal pullback attractor is attained by using the energy equation method and asymptotic compactness property. Furthermore, we construct a family of invariant Borel probability measures, which are supported on the pullback attractors. Specifically, when the external forcing terms are periodic in time, the periodic invariant measure can be obtained. Finally, as the delay approaches zero and system parameters tend to some numbers, the limit of the invariant measure sequences for this class of equations must be the invariant measure of the corresponding limit equations.

Keywords

Invariant Borel probability measureslimit behaviorspullback attractors

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35B41: Attractors 35Q30: Navier-Stokes equations 76D03: Existence, uniqueness, and regularity theory 76D05: Navier-Stokes equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 39
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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