Rongchan Zhu

activity

20102026

most citedSub and supercritical stochastic quasi-geostrophic equation

37 citations · 216 across the 55 of their papers we have counts for

collaborators

Showing math.PRShow all

45 papers · 1 filter

math.PR2024★ 2 cited

Langevin dynamics of lattice Yang-Mills-Higgs and applications

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper, we investigate the Langevin dynamics of various lattice formulations of the Yang--Mills--Higgs model, with an inverse Yang--Mills coupling $β$ and a Higgs parameter…

math.PR2023

Non-uniqueness of Leray-Hopf solutions for stochastic forced Navier-Stokes equations

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

We consider stochastic forced Navier--Stokes equations on $R^{3}$ starting from zero initial condition. The noise is linear multiplicative and the equations are perturbed…

math.PR2023

Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise

Martina Hofmanová, Xiaoyutao Luo, Rongchan Zhu +1

We consider a family of singular surface quasi-geostrophic equations $\partial_{t} θ + u \cdot \nabla θ = - ν (- Δ)^{γ /2} θ + (- Δ)^{α /2} ξ, u = \nabla^{⊥} (- Δ)^{- 1/2} θ,$ on $[0,\infty)…

math.PR2023★ 1 cited

Large $N$ limit and $1/ N$ expansion of invariant observables in $O (N)$ linear $σ$ -model via SPDE

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper, we continue the study of large $N$ problems for the Wick renormalized linear sigma model, i.e. $N$ -component $Φ^{4}$ model, in two spatial dimensions, using stochastic…

math.PR2022

Mean-field limit of Non-exchangeable interacting diffusions with singular kernels

Zhenfu Wang, Xianliang Zhao, Rongchan Zhu

The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed…

math.PR2022★ 6 cited

Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

We establish the existence of infinitely many stationary solutions, as well as ergodic stationary solutions, to the three dimensional Navier--Stokes and Euler equations in both det…

math.PR2022

A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

Martina Hofmanova, Rongchan Zhu, Xiangchan Zhu

We study the surface quasi-geostrophic equation with an irregular spatial perturbation $\partial_{t} θ + u \cdot \nabla θ = - ν (- Δ)^{γ /2} θ + ζ, u = \nabla^{⊥} (- Δ)^{- 1} θ,$ on $…

math.PR2022★ 12 cited

A stochastic analysis approach to lattice Yang--Mills at strong coupling

Hao Shen, Rongchan Zhu, Xiangchan Zhu

We develop a new stochastic analysis approach to the lattice Yang--Mills model at strong coupling in any dimension $d > 1$ , with t' Hooft scaling $β N$ for the inverse coupling streng…

math.PR2022★ 2 cited

A new derivation of the finite $N$ master loop equation for lattice Yang-Mills

Hao Shen, Scott A. Smith, Rongchan Zhu

We give a new derivation of the finite $N$ master loop equation for lattice Yang-Mills theory with structure group $S O (N)$ , $U (N)$ or $S U (N)$ . The $S O (N)$ case was initially proved…

math.PR2021

Singular kinetic equations and applications

Zimo Hao, Xicheng Zhang, Rongchan Zhu +1

In this paper we study singular kinetic equations on $R^{2 d}$ by the paracontrolled distribution method introduced in \cite{GIP15}. We first develop paracontrolled calculu…

math.PR2021★ 3 cited

An SPDE approach to perturbation theory of $Φ_{2}^{4}$ : asymptoticity and short distance behavior

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper we study the perturbation theory of $Φ_{2}^{4}$ model on the whole plane via stochastic quantization. We use integration by parts formula (i.e. Dyson-Schwinger equations)…

math.PR2021★ 1 cited

Gaussian fluctuations for interacting particle systems with singular kernels

Zhenfu Wang, Xianliang Zhao, Rongchan Zhu

We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation…

math.PR2021★ 4 cited

Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initia…

math.PR2021★ 13 cited

Large $N$ limit of the $O (N)$ linear sigma model in 3D

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper we study the large N limit of the $O (N)$ -invariant linear sigma model, which is a vector-valued generalization of the $Φ^{4}$ quantum field theory, on the three dimensi…

math.PR2020★ 10 cited

On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

We are concerned with the question of well-posedness of stochastic three dimensional incompressible Euler equations. In particular, we introduce a novel class of dissipative soluti…

math.PR2020★ 3 cited

Singular HJB equations with applications to KPZ on the real line

Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu

This paper is devoted to studying the Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which is not well-defined in the classical sense and shall be underst…

math.PR2020★ 7 cited

Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit

Dejun Luo, Rongchan Zhu

We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus $T^{2}$ , perturbed by multiplicative transport noise. The equation admits the white noise…

math.PR2019★ 13 cited

Non-uniqueness in law of stochastic 3D Navier--Stokes equations

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

We consider the stochastic Navier--Stokes equations in three dimensions and prove that the law of analytically weak solutions is not unique. In particular, we focus on three exampl…

math.PR2019

Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition

Wei Liu, Rongchan Zhu

In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDE where the coefficients satisfy a specific type Lyapunov condition instead…

math.PR2019★ 1 cited

Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus

Ting Ma, Rongchan Zhu

In this paper we discuss the convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations driven by space-time white noise on $\T$. First we prove that the co…

math.PR2019★ 3 cited

Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations

Huanyu Yang, Rongchan Zhu

We study the asymptotic limit, as $ε ↘ 0$ , of solutions of the stochastic Cahn-Hilliard equation: $$ \partial_t u^\varepsilon=Δ\left(-\varepsilonΔu^\varepsilon+\fra…

math.PR2019

Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise

Lubomir Banas, Huanyu Yang and, Rongchan Zhu

We study the the sharp interface limit of $ε$ -dependent two dimensional stochastic Cahn-Hilliard equation driven by space-time white noise and conservative noise as $\var…

math.PR2018★ 1 cited

Stochastic Heat Equations for infinite strings with Values in a Manifold

Xin Chen, Bo Wu, Rongchan Zhu +1

In the paper, we construct conservative Markov processes corresponding to the martingale solutions to the stochastic heat equation on $R^{+}$ or $R$ with values in…

math.PR2018★ 2 cited

Weak universality of the dynamical $Φ_{3}^{4}$ model on the whole space

Rongchan Zhu, Xiangchan Zhu

We prove the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on $R^{3}$ to the dynamical $Φ_{3}^{4}$ model by paracontrolled distribu…

Langevin dynamics of lattice Yang-Mills-Higgs and applications

Non-uniqueness of Leray-Hopf solutions for stochastic forced Navier-Stokes equations

Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise

Large N limit and 1/N expansion of invariant observables in O(N) linear σ-model via SPDE

Mean-field limit of Non-exchangeable interacting diffusions with singular kernels

Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations

A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

A stochastic analysis approach to lattice Yang--Mills at strong coupling

A new derivation of the finite N master loop equation for lattice Yang-Mills

Singular kinetic equations and applications

An SPDE approach to perturbation theory of Φ24​: asymptoticity and short distance behavior

Gaussian fluctuations for interacting particle systems with singular kernels

Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

Large N limit of the O(N) linear sigma model in 3D

On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations

Singular HJB equations with applications to KPZ on the real line

Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit

Non-uniqueness in law of stochastic 3D Navier--Stokes equations

Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition

Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus

Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations

Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise

Stochastic Heat Equations for infinite strings with Values in a Manifold

Weak universality of the dynamical Φ34​ model on the whole space

Large $N$ limit and $1/ N$ expansion of invariant observables in $O (N)$ linear $σ$ -model via SPDE

A new derivation of the finite $N$ master loop equation for lattice Yang-Mills

An SPDE approach to perturbation theory of $Φ_{2}^{4}$ : asymptoticity and short distance behavior

Large $N$ limit of the $O (N)$ linear sigma model in 3D

Weak universality of the dynamical $Φ_{3}^{4}$ model on the whole space