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Stability of Pullback Random Attractors for Stochastic 3D Navier-Stokes-Voight Equations with Delays

Stability of Pullback Random Attractors for Stochastic 3D Navier-Stokes-Voight Equations with Delays This paper is concerned with the limiting dynamics of stochastic retarded 3D non-autonomous Navier-Stokes-Voight (NSV) equations driven by Laplace-multiplier noise. We first prove the existence, uniqueness, forward compactness and forward longtime stability of pullback random attractors (PRAs). We then establish the upper semicontinuity of PRAs from non-autonomy to autonomy. Finally, we study the upper semicontinuity of PRAs under an analogue of Hausdorff semi-distance as the memory time tends to zero. Because of the solution has no higher regularity, the forward pullback asymptotic compactness of solutions in the state space is proved by the spectrum decomposition technique. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Stability of Pullback Random Attractors for Stochastic 3D Navier-Stokes-Voight Equations with Delays

Zhang, Qiangheng
Acta Applicandae Mathematicae , Volume 184 (1) – Apr 1, 2023
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Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-023-00560-y
Publisher site
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Abstract

This paper is concerned with the limiting dynamics of stochastic retarded 3D non-autonomous Navier-Stokes-Voight (NSV) equations driven by Laplace-multiplier noise. We first prove the existence, uniqueness, forward compactness and forward longtime stability of pullback random attractors (PRAs). We then establish the upper semicontinuity of PRAs from non-autonomy to autonomy. Finally, we study the upper semicontinuity of PRAs under an analogue of Hausdorff semi-distance as the memory time tends to zero. Because of the solution has no higher regularity, the forward pullback asymptotic compactness of solutions in the state space is proved by the spectrum decomposition technique.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Apr 1, 2023

Keywords: Stochastic delay NSV equation; Pullback random attractor; Stability; Upper semicontinuity; Spectrum decomposition; 37L55; 35B41; 35R60

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