4 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…
On the classification of invariant Gaussian measures for the 2D Euler equation
Ziyu Liu
We consider the two-dimensional incompressible Euler equation on with Gaussian random initial data having independent Fourier coefficients. For every , we prove…
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…
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…