1 citations · 1 across the 7 of their papers we have counts for
8 papers
The Wave Kinetic Theory for Quasilinear MMT Equation
Huaxiang Lü
We study the one-dimensional quasilinear Majda--McLaughlin--Tabak (MMT) equation on a large torus : \begin{align*} i \partial_t u +2π|\nabla|^σu +λ^{2}|\nabla|^β\left[ \left…
Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs
Huaxiang Lü
In this paper, we study distribution-dependent stochastic differential equations on the domain or , , of the form \begin{align*} {\rm…
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…
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 , driven by a -Wiener process of trace class: \begin{align*} \mathrm{d} u+\ma…
Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations
Huaxiang Lü, Michael Röckner, Xiangchan Zhu
We are concerned with the (stochastic) Lagrangian trajectories associated with Euler or Navier-Stokes equations. First, in the vanishing viscosity limit, we establish sharp non-uni…
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…
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…
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 . For the power index , we establish existence of…