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<p>In this paper, we investigate the existence and degenerate regularity of trajectory statistical solutions for the three-dimensional Boussinesq system with damping. We first establish that the existence of trajectory attractor holds, then we use it and natural translation semigroup to construct the trajectory statistical solutions in the trajectory space. Furthermore, we demonstrate that when the Grashof number related to the system remains sufficiently small, the trajectory statistical solution exhibits degenerate regularity.</p>

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Existence and degenerate regularity of the trajectory statistical solution for the 3D Boussinesq equations with damping

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Yuming Qin,
  • Huite Jiang

摘要

In this paper, we investigate the existence and degenerate regularity of trajectory statistical solutions for the three-dimensional Boussinesq system with damping. We first establish that the existence of trajectory attractor holds, then we use it and natural translation semigroup to construct the trajectory statistical solutions in the trajectory space. Furthermore, we demonstrate that when the Grashof number related to the system remains sufficiently small, the trajectory statistical solution exhibits degenerate regularity.