On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments

Briant, Marc; Einav, Amit

Abstract

The Boltzmann–Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Boltzmann–Nordheim equation for bosons, in dimension d⩾3. We show existence and uniqueness locally in time for any initial data in L∞(1+|v|s) with finite mass and energy, for a suitable s, as well as the instantaneous creation of moments of all order.

Citation

Briant, M., & Einav, A. (2016). On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments. Journal of Statistical Physics, 163(5), 1108–1156. https://doi.org/10.1007/s10955-016-1517-9

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2016
• Online Publication Date: Apr 12, 2016
• Publication Date: 2016-06
• Deposit Date: Nov 16, 2020
• Journal: Journal of Statistical Physics
• Print ISSN: 0022-4715
• Electronic ISSN: 1572-9613
• Publisher: Springer
• Volume: 163
• Issue: 5
• Pages: 1108–1156
• DOI: https://doi.org/10.1007/s10955-016-1517-9
• Public URL: https://durham-repository.worktribe.com/output/1257246