Regular measurable backward compact random attractor for $ g $-Navier-Stokes equation

Fuzhi Li; Dongmei Xu; Jiali Yu

doi:10.3934/cpaa.2020136

Article Contents

2020, Volume 19, Issue 6: 3137-3157. Doi: 10.3934/cpaa.2020136

This issue Previous Article Global existence and decay of solutions for hard potentials to the fokker-planck-boltzmann equation without cut-off Next Article Radial solutions for a class of Hénon type systems with partial interference with the spectrum

Regular measurable backward compact random attractor for $ g $-Navier-Stokes equation

1.
School of Mathematics & Computer Science, , Shangrao Normal University, Shangrao 334001, China
2.
School of Locomotive and Rolling Stock Engineering, Dalian Jiaotong University, Dalian 116028, China

^* Corresponding author
^* Corresponding author

Received: May 31, 2019

Revised: November 30, 2019

Published: March 2020

The first author is supported by Science and Technology Foundation of Jiangxi Education Department grant GJJ190880

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Abstract

In this paper, we study the backward compactness of random attractors, which describes the compactness of the union $ \cup_{s\leq\tau}\mathcal A(s,\omega) $ of random attractor sections over past times, $ \tau\in\mathbb R $. In particular, we prove the backward compactness and the regularity of random attractors for stochastic $ g $-Navier-Stokes equations under the condition that the force is backward tempered and backward limiting. The attraction universe in consideration is non-autonomous and consists of backward tempered sets.

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Mathematics Subject Classification: Primary: 37L55; Secondary: 35B41, 35R60.

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