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

Marc Briant (1) , Amit Einav (2)

1 Cambridge Center for Analysis
2 DPMMS - Department of Pure Mathematics and Mathematical Statistics

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.

Mots clés: Boltzmann-Nordheim equation; Kinetic model for bosons; Bose- Einstein condensattion; Subcritical solutions; Local Cauchy Problem

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Marc Briant, Amit Einav. On the Cauchy Problem for the Homogeneous Boltzmann-Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments. Journal of Statistical Physics, 2016, 163 (5), pp.1108-1156. ⟨10.1007/s10955-016-1517-9⟩. ⟨hal-01492026⟩