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math.PR2026
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…
math.PR2026
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…