Classical approximation of a linearized three waves kinetic equation

TL;DR

This paper derives and analyzes the fundamental solution of a classical approximation to a three waves kinetic equation relevant to bosonic gases near critical temperature, establishing its uniqueness and applicability to initial value problems.

Contribution

It provides the first explicit fundamental solution for this classical approximation and proves its uniqueness in a suitable distribution space.

Findings

Fundamental solution explicitly derived and characterized.

Proved uniqueness of the fundamental solution.

Applied to solve initial value problems for general data.

Abstract

The fundamental solution of the classical approximation of a three waves kinetic equation that happens in the kinetic theory of a condensed gas of bosons near the critical temperature is obtained. It is also proved to be unique in a suitable space of distributions and several of its properties are described. The fundamental solution is used to solve the initial value problem for a general class of initial data.