6 papers · 1 filter
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…
Asymptotic strong Feller and weak observability inequality
Ziyu Liu, Shengquan Xiang
For a class of non-autonomous linear SPDEs, we establish the equivalence among asymptotic regularization, weak observability, and approximate null controllability for the associate…
A note on the strong Feller property via the moment method
Ziyu Liu, Shengquan Xiang
This note studies the 1D stochastic heat equation driven by a one-dimensional Brownian motion. We prove that the associated Markov process satisfies the strong Feller property unde…
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 nonlinear Schrödinger equations perturbed by bounded degenerate noise
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang
We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schrödinger equations, perturbed by bounded noise acting on only two Fourier modes.…