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The Boltzmann-Nordheim equation is a modification of the Boltzmann equation,based on physical considerations, that describes the dynamics of thedistribution of particles in a quantum gas composed of bosons or fermions. Inthis work we investigate the Cauchy theory of the spatially homogeneousBoltzmann-Nordheim equation for bosons, in dimension $d\geq 3$. We showexistence 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.

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