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Qualitative properties for the 2‐D$D$ nonautonomous stochastic Navier–Stokes equations

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  • Dingshi Li
  • Shaoyue Mi

Abstract

We establish the pullback asymptotic compact of the family probability measures with respect to probability distributions of the solutions of the 2‐D$D$ nonautonomous stochastic Navier–Stokes equations, and prove the existence and uniqueness of a pullback measure attractor. The structures of pullback measure attractors is characterized by complete solutions, which is an extension of the notation of evolution systems of measures introduced and developed by Da Prato and Röckner in [Rendiconti Lincei‐Matematica e Applicazioni 17 (2006), no. 4, 397–403] and [Seminar on Stochastic Analysis, Random Fields and Applications, 115–122, Springer, 2007]. Moreover, for stochastic systems containing periodic deterministic forcing terms, we show the pullback measure attractors are also periodic under certain conditions.

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  • Dingshi Li & Shaoyue Mi, 2025. "Qualitative properties for the 2‐D$D$ nonautonomous stochastic Navier–Stokes equations," Mathematische Nachrichten, Wiley Blackwell, vol. 298(7), pages 2085-2104, July.
    • Handle: RePEc:bla:mathna:v:298:y:2025:i:7:p:2085-2104
    DOI: 10.1002/mana.12015
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