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

Abstract

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.

53 pages, 1 figure This new version contains the finite time condensation result that was previously contained in the article arXiv:1210.1664. Some misprints have been corrected and the presentation has been slightly modified at some places

References in corpus (3)

• Quantum Kinetic Theory of Condensate Growth---Comparison of Experiment and Theory
• Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases
• Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas

Cited by in corpus (3)

• A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. Part I: Local existence of solutions
• A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. Part II: Finite-time blow-up
• Convergence to the equilibrium state for Bose-Einstein 1-D Kac grazing limit model