Xiangchan Zhu

activity

20102026

most citedSub and supercritical stochastic quasi-geostrophic equation

37 citations · 222 across the 52 of their papers we have counts for

collaborators

53 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-ph2026

$P (Φ)_{2}$ Theory from many-body quantum Gibbs states

Phan Thành Nam, Zhilin Yang, Xiangchan Zhu

We derive the $P (Φ)_{2}$ measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding t…

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.PR2025

Gaussian Fluctuations for the Stochastic Landau-Lifshitz Navier-Stokes Equation in Dimension $D \geq 2$

Sotiris Kotitsas, Marco Romito, Zhilin Yang +1

We revisit the large-scale Gaussian fluctuations for the stochastic Landau-Lifshitz Navier-Stokes equation (LLNS) at and above criticality, using the method in \cite{CGT24}. With t…

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

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 $T^{2}$ \begin{align*} \dif…

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.PR2023

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…

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…

math.PR2022★ 1 cited

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 $d \geq 3$ . For the power index $r \in (1, \frac{3 d + 2}{d + 2})$ , we establish existence of…

math.PR2022★ 2 cited

Sharp non-uniqueness of solutions to stochastic Navier-Stokes equations

Weiquan Chen, Zhao Dong, Xiangchan Zhu

In this paper we establish a sharp non-uniqueness result for stochastic $d$ -dimensional ( $d \geq 2$ ) incompressible Navier-Stokes equations. First, for every divergence free initial…

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.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★ 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

P(Φ)2​ Theory from many-body quantum Gibbs states

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

Gaussian Fluctuations for the Stochastic Landau-Lifshitz Navier-Stokes Equation in Dimension D≥2

Φ34​ Theory from many-body quantum Gibbs states

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

Non-unique Ergodicity for the 2D Stochastic Navier-Stokes Equations with Derivative of Space-Time White Noise

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

Sharp Non-uniqueness of Solutions to 2D Navier-Stokes Equations with Space-Time White Noise

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

Global-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness

Sharp non-uniqueness of solutions to stochastic Navier-Stokes equations

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

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

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

$P (Φ)_{2}$ Theory from many-body quantum Gibbs states

Gaussian Fluctuations for the Stochastic Landau-Lifshitz Navier-Stokes Equation in Dimension $D \geq 2$

$Φ_{3}^{4}$ 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

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