Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains (2406.07460v3)

Published 11 Jun 2024 in math.PR and math.AP

Abstract: In this article, we discuss the existence and asymptotically autonomous robustness (AAR) (almost surely) of random attractors for 3D stochastic globally modified Navier-Stokes equations (SGMNSE) on Poincar\'e domains (which may be bounded or unbounded). Our aim is to investigate the existence and AAR of random attractors for 3D SGMNSE when the time-dependent forcing converges to a time-independent function under the perturbation of linear multiplicative noise as well as additive noise. The main approach is to provide a way to justify that, on some uniformly tempered universe, the usual pullback asymptotic compactness of the solution operators is uniform across an infinite time-interval $(-\infty,\tau]$. The backward uniform tail-smallness'' andflattening-property'' of the solutions over $(-\infty,\tau]$ have been demonstrated to achieve this goal. To the best of our knowledge, this is the first attempt to establish the existence as well as AAR of random attractors for 3D SGMNSE on unbounded domains.

Summary

We haven't generated a summary for this paper yet.