Huaxiang Lu

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math.PR2026

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs

Huaxiang LÃ¼

In this paper, we study distribution-dependent stochastic differential equations on the domain $O = T^{d}$ or $R^{d}$ , $d \geq 2$ , of the form \begin{align*} {\rm…

math.PR2025

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

Huaxiang LÃ¼, Lin LÃ¼, 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.PR2025

Sharp Non-uniqueness in Law for Stochastic Differential Equations on the Whole Space

Huaxiang LÃ¼, Michael RÃ¶ckner

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…