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math.PR2025
Sharp Non-uniqueness in Law for Stochastic Differential Equations on the Whole Space
Huaxiang Lü, Michael Röckner
In this paper, we investigate the stochastic differential equation on : \begin{align*} \dif X_t&=v(t,X_t)\dif t+\sqrt{2} \dif W_t. \end{align*} For any finite…
math.PR2024
Non-unique Ergodicity for the 2D Stochastic Navier-Stokes Equations with Derivative of Space-Time White Noise
Huaxiang Lü, Xiangchan Zhu
We prove existence of infinitely many stationary solutions as well as ergodic stationary solutions for the stochastic Navier-Stokes equations on \begin{align*} \dif…
math.PR2023
Sharp Non-uniqueness of Solutions to 2D Navier-Stokes Equations with Space-Time White Noise
Huaxiang Lü, Xiangchan Zhu
In this paper we are concerned with the 2D incompressible Navier-Stokes equations driven by space-time white noise. We establish existence of infinitely many global-in-time probabi…