Finite time blow-up and condensation for the bosonic Nordheim equation

• 成果类型: Article
• 署名作者: Escobedo, M.; Velazquez, J. J. L.
• 署名单位: University of Basque Country; Basque Center for Applied Mathematics (BCAM); University of Bonn
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0539-7
• 发表日期: 2015
• 页码: 761-847
• 关键词: uehling-uhlenbeck equation; bose-einstein particles; boltzmann-equation; kinetics; gas; statistics; TRANSITION; DYNAMICS

摘要

The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of classical solutions of the homogeneous bosonic Nordheim equation that blow up in finite time. We also prove finite time condensation for a class of weak solutions of the kinetic equation.