Asymptotically autonomous dynamics for non-autonomous stochastic $ g $-Navier-Stokes equation with additive noise

Fuzhi Li; Dongmei Xu

doi:10.3934/dcdsb.2022087

Article Contents

2023, Volume 28, Issue 1: 516-537. Doi: 10.3934/dcdsb.2022087

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Asymptotically autonomous dynamics for non-autonomous stochastic $ g $-Navier-Stokes equation with additive noise

Fuzhi Li and
Dongmei Xu^,

School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001 China

^* Corresponding author: Dongmei Xu, xudongmei@126.com
^* Corresponding author: Dongmei Xu, xudongmei@126.com

Received: July 31, 2021

Revised: January 31, 2022

Early access: May 2022

Published: January 2023

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Abstract

Both sufficient and necessary criteria for the existence of a bi-parametric attractor which attaches with forward compactness is established. Meanwhile, we prove that, under certain conditions, the components of the random attractor of a non-autonomous dynamical system can converge in time to those of the random attractor of the limiting autonomous dynamical system. As an application of the abstract theory, we show that the non-autonomous stochastic $ g $-Navier-Stokes (g-NS) equation possesses a forward compact random attractor such that it is forward asymptotically autonomous to a random attractor of the autonomous g-NS equation.

Keywords:

Stochastic $ g $-Navier-Stokes equation,
random attractor,
forward compactness,
asymptotically autonomous.

Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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