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<p>We study the nonlinear dynamics of the kinetic wave equation associated with the FPU problem and prove the stability of the non-singular Rayleigh–Jeans equilibria. The lack of a spectral gap for the linearized problem leads to polynomial decay, which we are able to leverage to obtain nonlinear stability.</p>

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Stability of Rayleigh–Jeans Equilibria in the Kinetic FPU Equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月7日

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  • Pierre Germain,
  • Joonhyun La,
  • Angeliki Menegaki

摘要

We study the nonlinear dynamics of the kinetic wave equation associated with the FPU problem and prove the stability of the non-singular Rayleigh–Jeans equilibria. The lack of a spectral gap for the linearized problem leads to polynomial decay, which we are able to leverage to obtain nonlinear stability.