On the Cauchy problem with large data for the space-dependent Boltzmann Nordheim equation III

TL;DR

This paper establishes existence, uniqueness, and stability of strong solutions for the space-dependent quantum Boltzmann Nordheim equation with large initial data, extending results to various force types and dimensions.

Contribution

It provides the first comprehensive analysis of strong solutions for the Cauchy problem with large data in the quantum Boltzmann Nordheim equation for Haldane statistics.

Findings

Existence of strong solutions under broad conditions.

Uniqueness and stability of solutions.

Conservation of mass, momentum, and energy.

Abstract

This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or three)-dimensional torus for three-dimensional velocities and pseudo-Maxwellian (resp. very soft) forces. The main results are existence, uniqueness and stability of solutions conserving mass, momentum, and energy, with the uniform bound exploding if the solutions are only local in time.