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math.AP2026
Exponential mixing for Korteweg-de Vries equation with localized noise
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang +1
We establish exponential mixing for the randomly forced and weakly damped KdV equation in . The noise is bounded, localized, and degenerate in high frequencies. Ou…
math.AP2025
Exponential mixing for the randomly forced NLS equation
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang +1
This paper investigates exponential mixing of the invariant measure for randomly forced nonlinear Schrödinger equation, with damping and random noise localized in space. Our study…
math.AP2024
Local large deviations for randomly forced nonlinear wave equations with localized damping
Yuxuan Chen, Ziyu Liu, Shengquan Xiang +1
We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish t…