40 citations · 135 across the 22 of their papers we have counts for
22 papers
Local Existence and Finite-Time Singularity Formation in the Vlasov-Poisson-Isotropic Landau System
Jin Woo Jang, Junsung Kim
The isotropic Landau (Coulomb) operator was introduced in kinetic theory by Krieger and Strain (Comm. Partial Differential Equations, 2012). In this work, we study the spatially in…
Optimal Convergence Estimate of the Limit from Inverse Power Potential to Hard Sphere Boltzmann Equation
Zheng-Nan Hu, Jin Woo Jang, Zheng-An Yao +1
The inverse power potential , generates the Boltzmann kernel with an angular singularity as . Jang-Kepka-Nota-Velázquez…
On the temperature distribution of a body heated by radiation
Jin Woo Jang, Juan J. L. Velázquez
In this paper, we study the temperature distribution of a body when the heat is transmitted only by radiation. The heat transmitted by convection and conduction is ignored. We cons…
Vanishing angular singularity limit to the hard-sphere Boltzmann equation
Jin Woo Jang, Bernhard Kepka, Alessia Nota +1
In this note we study Boltzmann's collision kernel for inverse power law interactions for in dimension . We prove the limit of the non-cutoff kernel…
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…
Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus
Jin Woo Jang, Robert M. Strain, Tak Kwong Wong
Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to b…
LTE and Non-LTE Solutions in Gases Interacting with Radiation
Jin Woo Jang, Juan J. L. Velázquez
In this paper, we study a class of kinetic equations describing radiative transfer in gases which include also the interaction of the molecules of the gas with themselves. We discu…
Asymptotic Stability of the Relativistic Boltzmann Equation without Angular Cut-off
Jin Woo Jang, Robert M. Strain
This paper is concerned with the relativistic Boltzmann equation without angular cutoff. We establish the global-in-time existence, uniqueness, and asymptotic stability for solutio…
Frequency multiplier estimates for the linearized relativistic Boltzmann operator without angular cutoff
Jin Woo Jang, Robert M. Strain
This paper is concerned with the relativistic Boltzmann equation without angular cutoff. The non-cutoff theory for the relativistic Boltzmann equation has been rarely studied even…
Sobolev Training for Physics Informed Neural Networks
Hwijae Son, Jin Woo Jang, Woo Jin Han +1
Physics Informed Neural Networks (PINNs) is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the sol…
The relativistic quantum Boltzmann equation near equilibrium
Gi-Chan Bae, Jin Woo Jang, Seok-Bae Yun
The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent…
Kinetic Models for Semiflexible Polymers in a Half-plane
Jin Woo Jang, Juan J. L. Velázquez
Based on a general discrete model for a semiflexible polymer chain, we introduce a formal derivation of a kinetic equation for semiflexible polymers in the half-plane via a continu…
The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach
Jae Yong Lee, Jin Woo Jang, Hyung Ju Hwang
The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In…
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…
On the Determinant Problem for the Relativistic Boltzmann Equation
James Chapman, Jin Woo Jang, Robert M. Strain
This article considers a long-outstanding open question regarding the Jacobian determinant for the relativistic Boltzmann equation in the center-of-momentum coordinates. For the Ne…
Averaging with a time-dependent perturbation parameter
David Fajman, Gernot Heißel, Jin Woo Jang
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillato…
Propagation of estimates for the Spatially Homogeneous Relativistic Boltzmann Equation
Jin Woo Jang, Seok-Bae Yun
In this paper, we prove the propagation of upper bounds for the spatially homogeneous relativistic Boltzmann equation for any . We consider the case of relativist…
Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach
Hyung Ju Hwang, Jin Woo Jang, Hyeontae Jo +1
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximate…
Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation
Jin Woo Jang, Robert M. Strain, Seok-Bae Yun
In this paper, we prove the propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. These bounds have been known to be a chall…
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…
Gain of regularity for the relativistic collision operator
Jin Woo Jang, Seok-Bae Yun
We study a regularity property for the gain part of the relativistic Boltzmann collision operator. Our assumptions on the collisional scattering kernel cover the full range of gene…
Global Classical Solutions to the Relativistic Boltzmann Equation without Angular Cut-off
Jin Woo Jang
We prove the unique existence and exponential decay of global in time classical solutions to the special relativistic Boltzmann equation without any angular cut-off assumptions wit…