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<p>This article is concerned with the asymptotic behavior of solutions for the 3D non-autonomous stochastic Kelvin–Voigt–Brinkman–Forchheimer equations driven by additive white noise on unbounded domains. The existence and uniqueness of tempered random attractors are proved for the equations. We also establish that the tempered random attractors are periodic when the non-autonomous external term is periodic in time. The energy equation method is employed to derive the pullback asymptotic compactness of solutions in order to overcome the difficulties caused by the non-compactness of Sobolev embeddings on unbounded domains.</p>

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Random Attractors for Non-autonomous Stochastic Kelvin–Voigt–Brinkman–Forchheimer Equations on Unbounded Domains

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Mengmeng Si,
  • Alain Miranville,
  • Rong Yang,
  • Xin-Guang Yang

摘要

This article is concerned with the asymptotic behavior of solutions for the 3D non-autonomous stochastic Kelvin–Voigt–Brinkman–Forchheimer equations driven by additive white noise on unbounded domains. The existence and uniqueness of tempered random attractors are proved for the equations. We also establish that the tempered random attractors are periodic when the non-autonomous external term is periodic in time. The energy equation method is employed to derive the pullback asymptotic compactness of solutions in order to overcome the difficulties caused by the non-compactness of Sobolev embeddings on unbounded domains.