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arXiv · 2303.18082

Polynomial Mixing for a Weakly Damped Stochastic Nonlinear Schr\"{o}dinger Equation

Jing Guo·Zhenxin Liu
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Abstract

This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schr\"{o}dinger 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, respectively, 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.

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Jing Guo, Zhenxin Liu. 2023-03-31. Polynomial Mixing for a Weakly Damped Stochastic Nonlinear Schr\"{o}dinger Equation. https://arxiv.org/abs/2303.18082

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