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<p>We prove the exponential mixing of invariant measure for Boussinesq equation on 2D torus, driven by the random Haar noise that is widely used in engineering sciences. The noise acts only in the temperature equation and is highly degenerate. Establishing approximate controllability for the linearized equation constitutes the bulk of our proof, combined with the general criterion at the level of random dynamical systems established in [<CitationRef CitationID="CR21">21</CitationRef>].</p>

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Exponential Mixing for the Boussinesq Equation with Haar Coloured Noise

  • 期刊论文

  • 发表日期：

    2025年12月27日

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  • Ziyu Liu,
  • Shengquan Xiang,
  • Jia-Cheng Zhao

摘要

We prove the exponential mixing of invariant measure for Boussinesq equation on 2D torus, driven by the random Haar noise that is widely used in engineering sciences. The noise acts only in the temperature equation and is highly degenerate. Establishing approximate controllability for the linearized equation constitutes the bulk of our proof, combined with the general criterion at the level of random dynamical systems established in [21].