5 papers
Exponential mixing for the stochastic Navier--Stokes equation with localized noise
Ziyu Liu, Shengquan Xiang, Zhifei Zhang
This paper studies the 2D Navier--Stokes equation on a bounded domain with Navier-slip boundary conditions, driven by spatially localized stationary forcing generated by a stochast…
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…
Exponential mixing for the stochastic Allen--Cahn equation with localized white noise
Ziyu Liu, Shengquan Xiang, Zhifei Zhang
This paper studies the 1D stochastic Allen--Cahn equation on a bounded domain driven by localized white noise. We prove that the associated Markov process admits a unique invariant…
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…
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…