Pullback V-Attractors of the Stochastic Calmed 3D Navier-Stokes Equations

Q: What type of study is this?

This is a Quantitative Study study.

Yuanfeng Duan; Anhui Gu

doi:10.48550/arxiv.2509.23553

September 28, 2025Open Access

Pullback V-Attractors of the Stochastic Calmed 3D Navier-Stokes Equations

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Key Points

The study shows the existence of a closed, measurable pullback absorbing set.
Using the Ornstein-Uhlenbeck process, we transformed the equations into a random form.
Galerkin approximation was applied to achieve global well-posedness of the calmed system.
The results indicate that the pullback flattening property leads to the existence of a pullback attractor.

Implication

This paper demonstrates global well-posedness and establishes pullback attractors in stochastic Navier-Stokes equations.

Abstract

In this paper, we investigate a calmed version of the 3D rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin approximation, we establish the global well-posedness of solutions for the calmed system. Then, we demonstrate the existence of a closed, measurable DV-pullback absorbing set. Finally, by proving the pullback flattening property, we obtain the existence of a DV-pullback attractor in \(V\).

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Cite This Study

Duan et al. (2025) studied this question.

synapsesocial.com/papers/68f6379bb481a140a36cf49a https://doi.org/10.48550/arxiv.2509.23553

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Pullback V-Attractors of the Stochastic Calmed 3D Navier-Stokes Equations

Key Points

Implication

Abstract

Discussion

Cite This Study

Pullback V-Attractors of the Stochastic Calmed 3D Navier-Stokes Equations

Key Points

Implication

Abstract

Discussion

Cite This Study

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