Lyapunov Functionals for the Enskog Equation

TL;DR

This paper introduces two Lyapunov functionals for the Enskog equation, one for particle interactions and another for solution stability, demonstrating convergence and stability of solutions over time.

Contribution

The paper presents novel Lyapunov functionals tailored for the Enskog equation, enabling analysis of particle interactions and solution stability.

Findings

Proves time-asymptotic convergence to collision-free motion.

Establishes $L^1$ stability of global classical solutions.

Provides tools for analyzing particle interactions in kinetic theory.

Abstract

Two Lyapunov functionals are presented for the Enskog equation. One is to describe interactions between particles with various velocities and another is to measure the $L^1$ distance between two classical solutions. The former yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the verification of the $L^1$ stability of global classical solutions.