5 papers
Instantaneous Exponential Ill-posedness of the BGK Model in a Half-Space with Inflow Boundary Conditions
Donghyun Lee, Sungbin Park, Sung-jun Son +1
In this paper, we study boundary-driven behavior of the BGK model and the Boltzmann equation in a half-space with vacuum initial data. For any and , we construct…
Global Well-posedness for the Multi-species Boltzmann Equation with Large Amplitude Initial Data
Gyounghun Ko, Myeong-Su Lee, Sung-Jun Son
This paper establishes the global well-posedness of the multi-species Boltzmann equation with large-amplitude initial data in the periodic domain . In contrast to the…
A Theory-guided Weighted Loss for solving the BGK model via Physics-informed neural networks
Gyounghun Ko, Sung-Jun Son, Seung Yeon Cho +1
While Physics-Informed Neural Networks offer a promising framework for solving partial differential equations, the standard loss formulation is fundamentally insufficient whe…
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…
Global Stability of the Boltzmann Equation for a Polyatomic Gas with Initial Data Allowing Large Oscillations
Gyounghun Ko, Sung-jun Son
In this paper, we consider the Boltzmann equation for a polyatomic gas. We establish that the mild solution to the Boltzmann equation on the torus is globally well-posed, provided…