33 citations · 46 across the 18 of their papers we have counts for
19 papers
Kinetic Wedge Layers and Diffusive Limit of Neutron Transport in Polygonal Domains
Zhimeng Ouyang, Lei Wu
We study the diffusive limit of the steady neutron transport equation with velocity-dependent in-flow boundary data in polygonal domains. On a bounded convex polygon, we construct…
Dynamics of Chemotactic Gliding-Aggregation in Myxobacteria on Bounded Domains: Stochastic Modeling, Analysis, and Deep Neural Network Simulations
Fugui Ma, Zhimeng Ouyang, Wenyi Tian +1
Bacterial chemotactic movement and collective aggregation have long attracted substantial interest in mathematical biology and applied modeling. Classical Keller--Segel-type system…
Lattice Approximations to NLS
Zhimeng Ouyang
In this paper, we prove that solutions of the discrete NLS lattice model for initial data with double frequency components converge to solutions of a coupled system of cubic…
The modified Korteweg--de Vries limit of the Ablowitz--Ladik system
Rowan Killip, Zhimeng Ouyang, Monica Visan +1
For slowly-varying initial data, solutions to the Ablowitz-Ladik system have been proven to converge to solutions of the cubic Schrödinger equation. In this paper we show that in t…
The Local-well-posedness of the relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition
Hongjie Dong, Yan Guo, Zhimeng Ouyang +1
We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain with the specular reflection condition. Our result covers the cas…
Conditional estimates for the non-cutoff Boltzmann equation in a bounded domain
Zhimeng Ouyang, Luis Silvestre
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular…
Diffusive Limit of the Boltzmann Equation in Bounded Domains
Zhimeng Ouyang, Lei Wu
The rigorous justification of the hydrodynamic limits of kinetic equations in bounded domains has been actively investigated in recent years. In spite of the progress for the diffu…
Diffusive Limit of the Unsteady Neutron Transport Equation in Bounded Domains
Zhimeng Ouyang
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady n…
Hilbert Expansion for Coulomb Collisional Kinetic Models
Zhimeng Ouyang, Lei Wu, Qinghua Xiao
The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau equation (r-LAN) are fundamental models that describe the dynamics of an electron gas. In this pap…
Continuum limit for the Ablowitz--Ladik system
Rowan Killip, Zhimeng Ouyang, Monica Visan +1
We show that solutions to the Ablowitz--Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely initial data. Furthermore, we consider initi…
Determining the collision kernel in the Boltzmann equation near the equilibrium
Li Li, Zhimeng Ouyang
We consider an inverse problem for the nonlinear Boltzmann equation near the equilibrium. Our goal is to determine the collision kernel in the Boltzmann equation from the knowledge…
Hilbert Expansion for the Relativistic Landau Equation
Zhimeng Ouyang, Lei Wu, Qinghua Xiao
In this paper, we study the local-in-time validity of the Hilbert expansion for the relativistic Landau equation. We justify that solutions of the relativistic Landau equation conv…
On the Quantum Boltzmann Equation near Maxwellian and Vacuum
Zhimeng Ouyang, Lei Wu
We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness wh…
Scattering map for the Vlasov-Poisson system
Patrick Flynn, Zhimeng Ouyang, Benoit Pausader +1
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as to asymptotic dynamics as $t\to…
The Vlasov-Poisson-Landau System with the Specular-Reflection Boundary Condition
Hongjie Dong, Yan Guo, Zhimeng Ouyang
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic…
Modified Wave Operators for the Wave-Klein-Gordon System
Zhimeng Ouyang
We consider a coupled Wave-Klein-Gordon system in 3D, which is a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields…
Asymptotic Analysis of Boltzmann Equation in Bounded Domains
Lei Wu, Zhimeng Ouyang
Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number $ε\rightar…
decay for the linearized Landau equation with the specular boundary condition
Yan Guo, Hyung Ju Hwang, Jin Woo Jang +1
In this paper, we develop an alternative approach to establish the decay estimate for the linearized Landau equation in a bounded domain with specular boundary condition. The…
The Landau equation with the specular reflection boundary condition
Yan Guo, Hyung Ju Hwang, Jin Woo Jang +1
The existence and stability of the Landau equation (1936) in a general bounded domain with a physical boundary condition is a long-outstanding open problem. This work proves the gl…