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

• Published in: Journal of statistical physics Vol. 163; no. 5; pp. 1108 - 1156
• Main Authors: Briant, Marc, Einav, Amit
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-06-2016; Springer; Springer Verlag
• Subjects: Analysis of PDEs; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Subcritical solutions; Boltzmann–Nordheim equation; Bose–Einstein condensation; Kinetic model for bosons; Local Cauchy problem; Boltzmann-Nordheim equation; Bose- Einstein condensattion; Local Cauchy Problem
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-016-1517-9

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.