On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Briant, M
Einav, A
Abstract
© 2016, Springer Science+Business Media New York. 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.
Description
Keywords
Boltzmann-Nordheim equation, Kinetic model for bosons, Bose-Einstein condensation, Subcritical solutions, Local Cauchy problem
Journal Title
Journal of Statistical Physics
Conference Name
Journal ISSN
0022-4715
1572-9613
1572-9613
Volume Title
163
Publisher
Springer
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/L002302/1)
Engineering and Physical Sciences Research Council (EP/H023348/1)
Engineering and Physical Sciences Research Council (EP/H023348/1)
The first author was supported by EPSRC Grant EP/H023348/1 for the Cambridge Centre for Analysis, and by the 150th Anniversary Postdoctoral Mobility Grant of the London Mathematical Society. The second author was supported by EPSRC Grant EP/L002302/1.