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<p>This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schrödinger equation with additive noise on a 1D bounded domain. The noise is white in time and smooth in space. We consider both focusing and defocusing nonlinearities, with exponents of the nonlinearity <i>σ</i> ∈ [0, 2) and <i>σ</i> ∈ [0, ∞), and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method. In the focusing case, our result generalizes the earlier results in [<CitationRef CitationID="CR12">12</CitationRef>], where <i>σ</i> = 1.</p>

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Polynomial mixing for a weakly damped stochastic nonlinear Schrödinger equation

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Jing Guo,
  • Zhenxin Liu

摘要

This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schrödinger equation with additive noise on a 1D bounded domain. The noise is white in time and smooth in space. We consider both focusing and defocusing nonlinearities, with exponents of the nonlinearity σ ∈ [0, 2) and σ ∈ [0, ∞), and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method. In the focusing case, our result generalizes the earlier results in [12], where σ = 1.