On the Cauchy problem for the homogeneous Boltzmann-Nordheim equation for bosons: local existence, uniqueness and creation of moments

29 Feb 2016  ·  Briant Marc, Einav Amit ·

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 $d\geq 3$... We show existence and uniqueness locally in time for any initial data in $L^\infty\left(1+|v|^s\right)$ with finite mass and energy, for a suitable $s$, as well as the instantaneous creation of moments of all order. read more

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Mathematical Physics Mathematical Physics