13 citations · 26 across the 9 of their papers we have counts for
9 papers
Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties
Juntao Huang, Liu Liu, Kunlun Qi +1
The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving cl…
Spectral convergence of a semi-discretized numerical system for the spatially homogeneous Boltzmann equation with uncertainties
Liu Liu, Kunlun Qi
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and…
On the kinetic description of the objective molecular dynamics
Richard D. James, Kunlun Qi, Li Wang
In this paper, we develop a multiscale hierarchy framework for objective molecular dynamics (OMD), a reduced order molecular dynamics with a certain symmetry, that connects it to t…
Convergence of the Fourier-Galerkin spectral method for the Boltzmann equation with uncertainties
Liu Liu, Kunlun Qi
It is well-known that the Fourier-Galerkin spectral method has been a popular approach for the numerical approximation of the deterministic Boltzmann equation with spectral accurac…
Moments creation for the inelastic Boltzmann equation for hard potentials without angular cutoff
Jin Woo Jang, Kunlun Qi
This paper is concerned with the inelastic Boltzmann equation without angular cutoff. We work in the spatially homogeneous case. We establish the global-in-time existence of measur…
On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials
Kunlun Qi
The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto-Wang-Yang, to the inelastic…
A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation
Jingwei Hu, Kunlun Qi, Tong Yang
Numerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional, nonlocal, and nonlinear collision integral. Over the past decade, the Fourie…
Measure Valued Solution to the Spatially Homogeneous Boltzmann Equation with Inelastic Long-Range Interactions
Kunlun Qi
This paper is to study the inelastic Boltzmann equation without Grad's angular cutoff assumption, where the well-posedness theory of the solution to the initial value problem is es…
A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
Jingwei Hu, Kunlun Qi
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in t…