Huaxiang Lu

most citedGlobal-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness

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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 $R^{d}, d \geq 2$ : \begin{align*} \dif X_t&=v(t,X_t)\dif t+\sqrt{2} \dif W_t. \end{align*} For any finite…

math.PR2025

A proof of Onsager's conjecture for the stochastic 3D Euler equations

Huaxiang Lü, Lin Lü, Rongchan Zhu

This paper investigates the stochastic 3D Euler equations on a periodic domain $T^{3}$ , driven by a $G G^{*}$ -Wiener process $B$ of trace class: \begin{align*} \mathrm{d} u+\ma…

math.PR2022★ 1 cited

Global-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness

Huaxiang Lü, Xiangchan Zhu

We are concerned with the power-law fluids driven by an additive stochastic forcing in dimension $d \geq 3$ . For the power index $r \in (1, \frac{3 d + 2}{d + 2})$ , we establish existence of…