One-dimensional diatomic Vlasov-Poisson system with oscillatory molecular bonds

TL;DR

This paper develops a kinetic model for diatomic plasma with oscillatory bonds, analyzing the existence and uniqueness of solutions, and extending local solutions to global ones through detailed oscillatory behavior analysis.

Contribution

It introduces a novel Vlasov-type model for diatomic plasma with oscillatory bonds and proves global existence and uniqueness of solutions.

Findings

Established a new kinetic model for diatomic plasma.

Proved global existence and uniqueness of solutions.

Analyzed oscillatory behavior near singular points.

Abstract

In this paper, we derive a Vlasov type kinetic model for diatomic plasma in which each ion consists of two atoms bonded through an oscillatory intermolecular force given by a singular Hooke potential. We then consider the existence and uniqueness of the classical solution to the proposed model. A careful analysis of the oscillatory behavior of atoms near singular points of the Hooke potential is carried out to extend the local-in-time solution to the global solution.