On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments
Journal of Statistical Physics
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Briant, M., & Einav, A. (2016). On the Cauchy Problem for the Homogeneous Boltzmann–Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments. Journal of Statistical Physics, 163 (5), 1108-1156. https://doi.org/10.1007/s10955-016-1517-9
© 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.
External DOI: https://doi.org/10.1007/s10955-016-1517-9
This record's URL: https://www.repository.cam.ac.uk/handle/1810/255110