100 citations · 588 across the 21 of their papers we have counts for
22 papers
Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary
Hongxu Chen, Chanwoo Kim
In this short note, we prove an -control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Espos…
Dynamical Billiard and a long-time behavior of the Boltzmann equation in general 3D toroidal domains
Gyounghun Ko, Chanwoo Kim, Donghyun Lee
Establishing global well-posedness and convergence toward equilibrium of the Boltzmann equation with specular reflection boundary condition has been one of the central questions in…
Hölder regularity of the Boltzmann equation past an obstacle
Chanwoo Kim, Donghyun Lee
Regularity and singularity of the solutions according to the shape of domains is a challenging research theme in the Boltzmann theory (\cite{Kim11,GKTT1}). In this paper, we prove…
Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space
Yunbai Cao, Chanwoo Kim
Following closely the classical works [8]-[12] by Glassey, Strauss, and Schaeffer, we present a version of the Glassey-Strauss representation for the Vlasov-Maxwell systems in a 3D…
Passage from the Boltzmann equation with Diffuse Boundary to the Incompressible Euler equation with Heat Convection
Yunbai Cao, Juhi Jang, Chanwoo Kim
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynam…
Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition
Hongxu Chen, Chanwoo Kim, Qin Li
The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a co…
On Some Recent Progress in the Vlasov-Poisson-Boltzmann System with Diffuse Reflection Boundary
Yunbai Cao, Chanwoo Kim
We discuss some recent development on the Vlasov-Poisson-Boltzmann system in bounded domains with diffuse reflection boundary condition. In addition we present a new regularity res…
Damping of kinetic transport equation with diffuse boundary condition
Jiaxin Jin, Chanwoo Kim
We prove that exponential moments of a fluctuation of the pure transport equation decay pointwisely almost as fast as when the domain is any general strictly convex subset…
Regularity of Stationary Boltzmann equation in Convex Domains
Hongxu Chen, Chanwoo Kim
Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order deri…
Incompressible Euler limit from Boltzmann equation with Diffuse Boundary Condition for Analytic data
Juhi Jang, Chanwoo Kim
A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition ha…
Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains
Yunbai Cao, Chanwoo Kim, Donghyun Lee
When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poi…
Decay of the Boltzmann equation with the specular boundary condition in non-convex cylindrical domains
Chanwoo Kim, Donghyun Lee
A basic question about the existence and stability of the Boltzmann equation in general non-convex domain with the specular reflection boundary condition has been widely open. In t…
Dynamics and stability of surfactant-driven surface waves
Chanwoo Kim, Ian Tice
In this paper we consider a layer of incompressible viscous fluid lying above a flat periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and…
The Boltzmann equation with specular boundary condition in convex domains
Chanwoo Kim, Donghyun Lee
We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum…
Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
Raffaele Esposito, Yan Guo, Chanwoo Kim +1
Despite its conceptual and practical importance, the rigorous derivation of the steady incompressible Navier-Stokes-Fourier system from the Boltzmann theory has been {an} outstandi…
BV-regularity of the Boltzmann equation in Non-Convex Domains
Yan Guo, Chanwoo Kim, Daniela Tonon +1
Consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a n…
Regularity of the Boltzmann Equation in Convex Domains
Yan Guo, Chanwoo Kim, Daniela Tonon +1
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the n…
Fourier Law and Non-Isothermal Boundary in the Boltzmann Theory
Raffaele Esposito, Yan Guo, Chanwoo Kim +1
In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the steady problem for the Boltzmann equation in a general bounded domain…
The Boltzmann equation near a rotational local Maxwellian
Chanwoo Kim, Seok-Bae Yun
In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium states called the rotational local Maxwellia…
The viscous surface-internal wave problem: global well-posedness and decay
Yanjin Wang, Ian Tice, Chanwoo Kim
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-di…
Boltzmann Equation with a Large Potential in a Periodic Box
Chanwoo Kim
The stability of the Maxwellian of the Boltzmann equation with a large amplitude external potential has been an important open problem. In this paper, we resolve this problem w…
Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains
Chanwoo Kim
The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Cons…