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<p>We consider a three dimensional globally modified 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 existence and uniqueness of strong solutions of the system. Then, we prove an upper bound on the number of determining nodes. Moreover, when the external force is time independent, we prove the existence of a global attractor for the continuous semigroup associated with the system, as well as the existence, uniqueness, and stability of a stationary solution.</p>

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Asymptotic behavior of solutions for the three dimensional globally modified Boussinesq model

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Tran Quang Thinh

摘要

We consider a three dimensional globally modified Boussinesq system with periodic boundary conditions, which is a particular case of the family of \(\alpha \) -models of turbulence. We first show the existence and uniqueness of strong solutions of the system. Then, we prove an upper bound on the number of determining nodes. Moreover, when the external force is time independent, we prove the existence of a global attractor for the continuous semigroup associated with the system, as well as the existence, uniqueness, and stability of a stationary solution.