Classical approximation of a linearized three waves kinetic equation

Abstract

The purpose of this work is to solve the Cauchy problem for the classical approximation of an isotropic linearized three waves kinetic equation that appears in the kinetic theory of a condensed gas of bosons near the critical temperature. The fundamental solution is obtained, it is proved to be unique in a suitable space of distributions, and some of its regularity and integrability properties are described. The initial value problem for integrable and locally bounded initial data is then solved. Classical solutions are obtained as functions, whose regularity depends on time and that satisfy the expected conservation of energy.