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<p>We consider a 3D regularized Boussinesq system with periodic boundary conditions, which is a particular case of the family of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-models of turbulence. We first show the determining projections and functionals for weak solutions of the system. Then, when the external force is time-independent, we give an upper bound for the fractal dimension of the global attractor for the continuous semigroup associated with the system.</p>

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On the Long-Time Behavior of Solutions to a 3D Regularized Boussinesq System

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Tran Quang Thinh,
  • Vu Manh Toi

摘要

We consider a 3D regularized Boussinesq system with periodic boundary conditions, which is a particular case of the family of \(\alpha \) -models of turbulence. We first show the determining projections and functionals for weak solutions of the system. Then, when the external force is time-independent, we give an upper bound for the fractal dimension of the global attractor for the continuous semigroup associated with the system.