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

57 papers

math-ph2026

Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D

Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu

In this paper we derive the time-dependent correlation functions of the renormalized Hartree NLS equation on the torus $T^{d}$ , $d = 2, 3$ , from the corresponding bosonic many-b…

math.AP2026

Global well-posedness for generalized parabolic Anderson model on the whole plane

Hao Shen, Rongchan Zhu, Xiangchan Zhu

For every $0<κ<\sqrt{5}-2$, we prove global existence for the two-dimensional generalized parabolic Anderson model on the whole plane $R^{2}$ with nonlinearity $F\in C_b^2(…

math-ph2026

Derivation of Gibbs measure from Gibbs state with the fractional Bessel interaction in Two Dimensions

Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu

We derive the classical Gibbs measure on $T^{2}$ associated with the fractional Bessel interaction potential $v_{β} (k) = ⟨ k ⟩^{- β}$ from a renormalized gra…

math-ph2025

$Φ_{3}^{4}$ Theory from many-body quantum Gibbs states

Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu

We derive the $Φ_{3}^{4}$ measure on the torus as a rigorous limit of the quantum Gibbs state of an interacting Bose gas. To be precise, starting from many-body quantum mechanics, wher…

math.AP2024

Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus

Hao Shen, Rongchan Zhu, Xiangchan Zhu

This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $R^{+} \times T^{2}$ within the framework of paracontrolled…

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.AP2023★ 3 cited

Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations

Martina Hofmanová, Umberto Pappalettera, Rongchan Zhu +1

We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ sati…

math.AP2023

Kolmogorov $4/5$ law for the forced 3D Navier-Stokes equations

Martina Hofmanová, Umberto Pappalettera, Rongchan Zhu +1

We identify a sufficient condition under which solutions to the 3D forced Navier--Stokes equations satisfy an $L^{p}$ -in-time version of the Kolmogorov 4/5 law for the behavior of th…

cs.LG2023★ 7 cited

Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

Rui Zhang, Qi Meng, Rongchan Zhu +5

In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existi…

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…

physics.flu-dyn2022

Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equations

Rui Zhang, Peiyan Hu, Qi Meng +5

Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations,…

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…

cs.LG2022★ 8 cited

Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs

Peiyan Hu, Qi Meng, Bingguang Chen +6

Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generation…

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.AP2021★ 5 cited

Global existence and non-uniqueness for 3D Navier--Stokes equations with space-time white noise

Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu

We establish global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In t…

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…

Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D

Global well-posedness for generalized parabolic Anderson model on the whole plane

Derivation of Gibbs measure from Gibbs state with the fractional Bessel interaction in Two Dimensions

Φ34​ Theory from many-body quantum Gibbs states

Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus

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

Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations

Kolmogorov 4/5 law for the forced 3D Navier-Stokes equations

Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation

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

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

Deep Random Vortex Method for Simulation and Inference of Navier-Stokes 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

Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs

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

Global existence and non-uniqueness for 3D Navier--Stokes equations with space-time white noise

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

$Φ_{3}^{4}$ Theory from many-body quantum Gibbs states

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

Kolmogorov $4/5$ law for the forced 3D Navier-Stokes equations

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