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 $\sigma\in[0,2)$ and $\sigma\in[0,\infty)$, 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 $\sigma=1$.
Jing GUO
,
Zhenxin LIU
. POLYNOMIAL MIXING FOR A WEAKLY DAMPED STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION[J]. Acta mathematica scientia, Series B, 2025
, 45(5)
: 2029
-2059
.
DOI: 10.1007/s10473-025-0513-z
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