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math.AP2026
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…
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…
math.AP2024
Exponential mixing for random nonlinear wave equations: weak dissipation and localized control
Ziyu Liu, Dongyi Wei, Shengquan Xiang +2
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equation…