33 citations · 104 across the 43 of their papers we have counts for
45 papers
A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains
Zhenxin Liu, Wenhu Zhong
For any , we construct -Hölder-continuous martingale solutions to the two-dimensional stochastic incompressible Euler equations. These marti…
Averaging Principle and Pullback Attractor Convergence for McKean--Vlasov Stochastic Reaction--Diffusion Equations
Honglei Chen, Mengyu Cheng, Zhenxin Liu
We establish three averaging principles for distribution-dependent stochastic reaction--diffusion equations with rapidly oscillating coefficients on the torus , $d\le3…
Continuity of measure-theoretic entropy for stochastic differential equations
Zhenxin Liu, Lixin Zhang
For stochastic differential equations, we establish a relationship between the measure-theoretic entropy of the stochastic flow and the rate of volume growth of stable submanifolds…
A criterion for the well-posedness of McKean-Vlasov stochastic differential equations
Zhenxin Liu, Ziting Liu
We establish strong existence and pathwise uniqueness for McKean-Vlasov stochastic differential equations with coefficients satisfying a distribution-dependent Lyapunov condition.…
Convergence rates of Wasserstein gradient flows for nonlinear Fokker-Planck equations with mobility and related inequalities
Zhenxin Liu, Xuewei Wang
For nonlinear Fokker-Planck equations with mobility, the Wasserstein gradient flow structure is described by the generalized relative entropy as the energy functional and the modif…
Continuity and Discontinuity of McKean-Vlasov Phase Transitions via Bifurcation Theory
Junlang Hu, Zhenxin Liu
It is well known that the McKean-Vlasov stochastic differential equation with a symmetric double-well potential exhibits a continuous phase transition. In contrast, for an asymmetr…