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Fluctuating Kinetic Theory: A Poissonian Stochastic Boltzmann Equation
Zhengyan Wu
We introduce a nonlinear Poissonian fluctuating Boltzmann equation whose noise encodes both the fluctuations and the path large-deviation rate function of the underlying hard-spher…
Dean-Kawasaki Equation with Biot-Savart and Keller-Segel Interactions: Existence and Large Deviations
Xiaohao Ji, Yue Sun, Zhengyan Wu
We establish the existence of probabilistically weak, renormalized kinetic solutions to the Dean--Kawasaki equation with singular interaction kernels, including those of Biot--Sava…
Learning Equilibrium Fluctuation Expansions from Overdamped Langevin Dynamics
Lin Wang, Zhengyan Wu
We study higher-order small-noise fluctuation expansions for the overdamped Langevin dynamics in a quartic double-well potential. Assuming that the initial data admits a suitable e…
The Incompressible Navier--Stokes--Fourier System with Thermal Noise
Benjamin Gess, Max Sauerbrey, Zhengyan Wu
We establish a solution theory for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible determini…
Ergodicity for the Dean--Kawasaki Equation with Dirichlet Boundary Conditions: Taming the Square-Root
Shyam Popat, Zhengyan Wu
In this paper, we establish the ergodicity of generalized Dean--Kawasaki equations with correlated noise and Dirichlet boundary conditions. In contrast to the ergodicity results of…
Fluctuating Hydrodynamics of the Ising-Kac-Kawasaki Model and Nonlinear Fluctuations Near Criticality
Zhengyan Wu
We study the scaling limit behavior of a family of conservative SPDEs as the fluctuating Ising-Kac-Kawasaki dynamics. Precisely, we show that there exists a sequence of the one-dim…
Kinetic Theory with Fluctuations: Well-Posedness of The Vlasov--Fokker--Planck--Dean--Kawasaki Equations
Zimo Hao, Zhengyan Wu, Johannes Zimmer
We study Vlasov--Fokker--Planck--Dean--Kawasaki equations driven by correlated conservative noise. For regular noise coefficients and bounded nonlocal interactions, we establish pr…
Probabilistic Approaches to The Energy Equality in Forced Surface Quasi-Geostrophic Equations
Lin Wang, Zhengyan Wu
We explore probabilistic approaches to the deterministic energy equality for the forced Surface Quasi-Geostrophic (SQG) equation on a torus. First, we prove the zero-noise dynamica…
Higher Order Fluctuation Expansions for Nonlinear Stochastic Heat Equations in Singular Limits
Benjamin Gess, Zhengyan Wu, Rangrang Zhang
Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions descri…
Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality
Benjamin Gess, Daniel Heydecker, Zhengyan Wu
The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise…