Bi-spatial pullback random attractors of stochastic ϱ -Navier–Stokes equations: Existence, regularity and finite fractal dimension

作者：Yunshun Wu, Nguyen Tien Da, Hailang Bai · 发表于：Journal of Mathematical Physics · 年份：2025 · DOI：10.1063/5.0239336 · 被引用次数：1 · 研究领域：Stability and Controllability of Differential Equations、Advanced Mathematical Modeling in Engineering、Fluid Dynamics and Turbulent Flows

This paper is concerned with the existence, regularity as well as finite fractal dimension of pullback random attractors of a wide class of non-autonomous stochastic ϱ-Navier-Stokes equations driven by additive noise. The existence and uniqueness of pullback random attractors of the equations are established in an appropriate ϱ-weighted L2-subspace Hϱ. This attractor is proved to be a bi-spatial attractor that is compact, measurable in another ϱ-weighted H01-subspace Vϱand attracts all random subsets of Hϱunder the topology of Vϱ. The finite fractal dimension of the bi-spatial random attractors is also derived without differentiating the system with respect to time. A spectrum decomposition method is employed to derive the pullback flattening properties (see Kloeden and Langa [Proc. R. Soc. A 463, 163–181(2007)]) of the solutions in Vϱin order to overcome the lack of higher regularity than Vϱand the almost sure non-differentiability of the sample paths of the Wiener process. The results of this article are new even when the stochastic ϱ-Navier-Stokes equation reduces to the standard stochastic Navier-Stokes equation.