Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LONG-TIME BEHAVIOR OF A FAMILY OF INCOMPRESSIBLE THREE-DIMENSIONAL LERAY-α-LIKE MODELS

  • Anh, Cung The (Department of Mathematics Hanoi National University of Education) ;
  • Thuy, Le Thi (Department of Mathematics Electric Power University) ;
  • Tinh, Le Tran (Department of Natural Sciences Hong Duc University)
  • Received : 2020.05.27
  • Accepted : 2021.07.23
  • Published : 2021.09.30
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Abstract

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃1 and 𝜃2. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

Keywords

Acknowledgement

This work is supported by Vietnam Ministry of Education and Training under grant number B2021-SPH-15.

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