On the Cauchy problem with large data for a space-dependent Boltzmann-Nordheim boson equation II

TL;DR

This paper establishes the existence, uniqueness, and stability of strong solutions for a space-dependent Boltzmann-Nordheim boson equation with large initial data, ensuring conservation laws and qualitative boundedness.

Contribution

It provides the first rigorous analysis of strong solutions for large data in a space-inhomogeneous boson equation with pseudo-Maxwellian forces.

Findings

Existence and uniqueness of strong solutions for large initial data.

Solutions conserve mass, momentum, and energy.

Solutions exhibit qualitative boundedness and stability.

Abstract

This paper studies a space-inhomogeneous Boltzmann-Nordheim equation with pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem in a setting with large bounded L1 initial data. The main results are existence, uniqueness, stability and qualitative boundedness features for solutions conserving mass, momentum and energy.