4 papers
A Physics-Informed, Global-in-Time Neural Particle Method for the Spatially Homogeneous Landau Equation
Minseok Kim, Sung-Jun Son, Yeoneung Kim +1
We propose a physics-informed neural particle method (PINN--PM) for the spatially homogeneous Landau equation. The method adopts a Lagrangian interacting-particle formulation and j…
Ill-posedness of the Boltzmann-BGK model in the exponential class
Donghyun Lee, Sungbin Park, Seok-Bae Yun
BGK (Bhatnagar-Gross-Krook) model is a relaxation-type model of the Boltzmann equation, which is popularly used in place of the Boltzmann equation in physics and engineering. In th…
Global solutions in for the Boltzmann equation in bounded domains
Dingqun Deng, Jong-in Kim, Donghyun Lee
The existence theory for solutions to the Boltzmann equation in bounded domains has primarily been developed within uniformly bounded function classes, such as ,…
On the large amplitude solution of the Boltzmann equation with large external potential and boundary effects
Jong-in Kim, Donghyun Lee
The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a boun…