10 papers
Gradient flow approach to Landau equation: A cross-product structure
Manh Hong Duong, Zihui He
We introduce a cross-product Landau gradient that commutes with Gaussian mollification. For the hard-potential interaction kernels of the form $A(|v-v_*|)\sim \langle v-v_*\rangle^…
The Homogeneous Landau Equation with Regularised Thermal Noise
Manh Hong Duong, Zihui He, Zhengyan Wu
We introduce and analyze a fluctuating homogeneous Landau equation with regularised thermal noise. The model is motivated by the nonlocal gradient flow structure of the determinist…
Unified Formulation and Asymptotic Limits of Inhomogeneous Kinetic Models within GENERIC
Manh Hong Duong, Zihui He
In this paper, we study a general class of inhomogeneous kinetic models that unifies fundamental models in both the statistical physics of particles and of waves, namely the kineti…
Multi-species kinetic models: GENERIC formulation and Fisher information
Manh Hong Duong, Zihui He
In this paper, we study the GENERIC structures of multi-species spatially inhomogeneous Boltzmann and Landau equations with Bose-Einstein, Maxwell-Boltzmann, and Fermi-Dirac statis…
On a fuzzy Landau Equation: Part III. The grazing collision limit
Manh Hong Duong, Boris Golubkov, Zihui He
In this paper, we study the grazing limit from the non-cutoff fuzzy Boltzmann equations to the fuzzy Landau equation, where particles interact through delocalised collisions. We sh…
GENERIC formulation and small-angle limit for Kinetic wave equations
Manh Hong Duong, Zihui He
In this paper, we formulate the three-wave and four-wave kinetic equations into the GENERIC framework and formally derive a small-angle limit for the four-wave equation. This limit…
On a fuzzy Landau Equation: Part II. Solvability results
Manh Hong Duong, Zihui He
This article is the second in a series of our works on the fuzzy Landau equation, where particles interact via delocalised Coulomb collisions. In this work, we focus on the existen…
Passing to the limit in fuzzy Boltzmann equations
Matthias Erbar, Zihui He
We study a fuzzy Boltzmann equation, where collisions are delocalised and modulated by a spatial kernel. We show that as the spatial kernel converges to a delta distribution, the s…
On a fuzzy Landau Equation: Part I. A variational approach
Manh Hong Duong, Zihui He
This article is the first in a series of works on the fuzzy Landau equation, where particles interact through delocalised Coulomb collisions. Here, we establish a variational chara…
A variational approach to a fuzzy Boltzmann equation
Matthias Erbar, Zihui He
We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of s…