Local classical solutions of a three excitations kinetic system for a homogeneous condensed gas of bosons

TL;DR

This paper proves short-time existence of classical solutions for a kinetic system modeling interactions in a bosonic gas near the critical temperature, providing insights into the system's qualitative behavior.

Contribution

It establishes the existence of classical solutions for a three excitations kinetic system, a novel model describing boson interactions near condensation.

Findings

Short-time classical solutions are proven to exist.

Qualitative properties of solutions are analyzed.

The model links condensate interactions with normal gas excitations.

Abstract

Short time existence of classical solutions is proved for a system of equations that involves a three excitations kinetic operator. The system is related to the description of a gas of bosons below but close to the critical temperature, where the three excitations integral aims at describing the interaction between the particles in the condensate and the excitations in the normal gas. Some qualitative properties of the solutions are obtained.